xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 98b658c4f30b83cdf7437c1c654f5e1950040f05)
1 
2 
3 #include <../src/mat/impls/aij/mpi/mpiaij.h>   /*I "petscmat.h" I*/
4 #include <petsc/private/vecimpl.h>
5 #include <petsc/private/isimpl.h>
6 #include <petscblaslapack.h>
7 #include <petscsf.h>
8 
9 /*MC
10    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
11 
12    This matrix type is identical to MATSEQAIJ when constructed with a single process communicator,
13    and MATMPIAIJ otherwise.  As a result, for single process communicators,
14   MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
15   for communicators controlling multiple processes.  It is recommended that you call both of
16   the above preallocation routines for simplicity.
17 
18    Options Database Keys:
19 . -mat_type aij - sets the matrix type to "aij" during a call to MatSetFromOptions()
20 
21   Developer Notes: Subclasses include MATAIJCUSP, MATAIJCUSPARSE, MATAIJPERM, MATAIJCRL, and also automatically switches over to use inodes when
22    enough exist.
23 
24   Level: beginner
25 
26 .seealso: MatCreateAIJ(), MatCreateSeqAIJ(), MATSEQAIJ, MATMPIAIJ
27 M*/
28 
29 /*MC
30    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
31 
32    This matrix type is identical to MATSEQAIJCRL when constructed with a single process communicator,
33    and MATMPIAIJCRL otherwise.  As a result, for single process communicators,
34    MatSeqAIJSetPreallocation() is supported, and similarly MatMPIAIJSetPreallocation() is supported
35   for communicators controlling multiple processes.  It is recommended that you call both of
36   the above preallocation routines for simplicity.
37 
38    Options Database Keys:
39 . -mat_type aijcrl - sets the matrix type to "aijcrl" during a call to MatSetFromOptions()
40 
41   Level: beginner
42 
43 .seealso: MatCreateMPIAIJCRL,MATSEQAIJCRL,MATMPIAIJCRL, MATSEQAIJCRL, MATMPIAIJCRL
44 M*/
45 
46 PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
47 {
48   PetscErrorCode ierr;
49   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)M->data;
50 
51   PetscFunctionBegin;
52   if (mat->A) {
53     ierr = MatSetBlockSizes(mat->A,rbs,cbs);CHKERRQ(ierr);
54     ierr = MatSetBlockSizes(mat->B,rbs,1);CHKERRQ(ierr);
55   }
56   PetscFunctionReturn(0);
57 }
58 
59 PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M,IS *keptrows)
60 {
61   PetscErrorCode  ierr;
62   Mat_MPIAIJ      *mat = (Mat_MPIAIJ*)M->data;
63   Mat_SeqAIJ      *a   = (Mat_SeqAIJ*)mat->A->data;
64   Mat_SeqAIJ      *b   = (Mat_SeqAIJ*)mat->B->data;
65   const PetscInt  *ia,*ib;
66   const MatScalar *aa,*bb;
67   PetscInt        na,nb,i,j,*rows,cnt=0,n0rows;
68   PetscInt        m = M->rmap->n,rstart = M->rmap->rstart;
69 
70   PetscFunctionBegin;
71   *keptrows = 0;
72   ia        = a->i;
73   ib        = b->i;
74   for (i=0; i<m; i++) {
75     na = ia[i+1] - ia[i];
76     nb = ib[i+1] - ib[i];
77     if (!na && !nb) {
78       cnt++;
79       goto ok1;
80     }
81     aa = a->a + ia[i];
82     for (j=0; j<na; j++) {
83       if (aa[j] != 0.0) goto ok1;
84     }
85     bb = b->a + ib[i];
86     for (j=0; j <nb; j++) {
87       if (bb[j] != 0.0) goto ok1;
88     }
89     cnt++;
90 ok1:;
91   }
92   ierr = MPIU_Allreduce(&cnt,&n0rows,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)M));CHKERRQ(ierr);
93   if (!n0rows) PetscFunctionReturn(0);
94   ierr = PetscMalloc1(M->rmap->n-cnt,&rows);CHKERRQ(ierr);
95   cnt  = 0;
96   for (i=0; i<m; i++) {
97     na = ia[i+1] - ia[i];
98     nb = ib[i+1] - ib[i];
99     if (!na && !nb) continue;
100     aa = a->a + ia[i];
101     for (j=0; j<na;j++) {
102       if (aa[j] != 0.0) {
103         rows[cnt++] = rstart + i;
104         goto ok2;
105       }
106     }
107     bb = b->a + ib[i];
108     for (j=0; j<nb; j++) {
109       if (bb[j] != 0.0) {
110         rows[cnt++] = rstart + i;
111         goto ok2;
112       }
113     }
114 ok2:;
115   }
116   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),cnt,rows,PETSC_OWN_POINTER,keptrows);CHKERRQ(ierr);
117   PetscFunctionReturn(0);
118 }
119 
120 PetscErrorCode  MatDiagonalSet_MPIAIJ(Mat Y,Vec D,InsertMode is)
121 {
122   PetscErrorCode    ierr;
123   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*) Y->data;
124 
125   PetscFunctionBegin;
126   if (Y->assembled && Y->rmap->rstart == Y->cmap->rstart && Y->rmap->rend == Y->cmap->rend) {
127     ierr = MatDiagonalSet(aij->A,D,is);CHKERRQ(ierr);
128   } else {
129     ierr = MatDiagonalSet_Default(Y,D,is);CHKERRQ(ierr);
130   }
131   PetscFunctionReturn(0);
132 }
133 
134 
135 PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M,IS *zrows)
136 {
137   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)M->data;
138   PetscErrorCode ierr;
139   PetscInt       i,rstart,nrows,*rows;
140 
141   PetscFunctionBegin;
142   *zrows = NULL;
143   ierr   = MatFindZeroDiagonals_SeqAIJ_Private(aij->A,&nrows,&rows);CHKERRQ(ierr);
144   ierr   = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
145   for (i=0; i<nrows; i++) rows[i] += rstart;
146   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)M),nrows,rows,PETSC_OWN_POINTER,zrows);CHKERRQ(ierr);
147   PetscFunctionReturn(0);
148 }
149 
150 PetscErrorCode MatGetColumnNorms_MPIAIJ(Mat A,NormType type,PetscReal *norms)
151 {
152   PetscErrorCode ierr;
153   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)A->data;
154   PetscInt       i,n,*garray = aij->garray;
155   Mat_SeqAIJ     *a_aij = (Mat_SeqAIJ*) aij->A->data;
156   Mat_SeqAIJ     *b_aij = (Mat_SeqAIJ*) aij->B->data;
157   PetscReal      *work;
158 
159   PetscFunctionBegin;
160   ierr = MatGetSize(A,NULL,&n);CHKERRQ(ierr);
161   ierr = PetscCalloc1(n,&work);CHKERRQ(ierr);
162   if (type == NORM_2) {
163     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
164       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]*a_aij->a[i]);
165     }
166     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
167       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]*b_aij->a[i]);
168     }
169   } else if (type == NORM_1) {
170     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
171       work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
172     }
173     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
174       work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
175     }
176   } else if (type == NORM_INFINITY) {
177     for (i=0; i<a_aij->i[aij->A->rmap->n]; i++) {
178       work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
179     }
180     for (i=0; i<b_aij->i[aij->B->rmap->n]; i++) {
181       work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]),work[garray[b_aij->j[i]]]);
182     }
183 
184   } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Unknown NormType");
185   if (type == NORM_INFINITY) {
186     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
187   } else {
188     ierr = MPIU_Allreduce(work,norms,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
189   }
190   ierr = PetscFree(work);CHKERRQ(ierr);
191   if (type == NORM_2) {
192     for (i=0; i<n; i++) norms[i] = PetscSqrtReal(norms[i]);
193   }
194   PetscFunctionReturn(0);
195 }
196 
197 PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A,IS *is)
198 {
199   Mat_MPIAIJ      *a  = (Mat_MPIAIJ*)A->data;
200   IS              sis,gis;
201   PetscErrorCode  ierr;
202   const PetscInt  *isis,*igis;
203   PetscInt        n,*iis,nsis,ngis,rstart,i;
204 
205   PetscFunctionBegin;
206   ierr = MatFindOffBlockDiagonalEntries(a->A,&sis);CHKERRQ(ierr);
207   ierr = MatFindNonzeroRows(a->B,&gis);CHKERRQ(ierr);
208   ierr = ISGetSize(gis,&ngis);CHKERRQ(ierr);
209   ierr = ISGetSize(sis,&nsis);CHKERRQ(ierr);
210   ierr = ISGetIndices(sis,&isis);CHKERRQ(ierr);
211   ierr = ISGetIndices(gis,&igis);CHKERRQ(ierr);
212 
213   ierr = PetscMalloc1(ngis+nsis,&iis);CHKERRQ(ierr);
214   ierr = PetscMemcpy(iis,igis,ngis*sizeof(PetscInt));CHKERRQ(ierr);
215   ierr = PetscMemcpy(iis+ngis,isis,nsis*sizeof(PetscInt));CHKERRQ(ierr);
216   n    = ngis + nsis;
217   ierr = PetscSortRemoveDupsInt(&n,iis);CHKERRQ(ierr);
218   ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
219   for (i=0; i<n; i++) iis[i] += rstart;
220   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),n,iis,PETSC_OWN_POINTER,is);CHKERRQ(ierr);
221 
222   ierr = ISRestoreIndices(sis,&isis);CHKERRQ(ierr);
223   ierr = ISRestoreIndices(gis,&igis);CHKERRQ(ierr);
224   ierr = ISDestroy(&sis);CHKERRQ(ierr);
225   ierr = ISDestroy(&gis);CHKERRQ(ierr);
226   PetscFunctionReturn(0);
227 }
228 
229 /*
230     Distributes a SeqAIJ matrix across a set of processes. Code stolen from
231     MatLoad_MPIAIJ(). Horrible lack of reuse. Should be a routine for each matrix type.
232 
233     Only for square matrices
234 
235     Used by a preconditioner, hence PETSC_EXTERN
236 */
237 PETSC_EXTERN PetscErrorCode MatDistribute_MPIAIJ(MPI_Comm comm,Mat gmat,PetscInt m,MatReuse reuse,Mat *inmat)
238 {
239   PetscMPIInt    rank,size;
240   PetscInt       *rowners,*dlens,*olens,i,rstart,rend,j,jj,nz = 0,*gmataj,cnt,row,*ld,bses[2];
241   PetscErrorCode ierr;
242   Mat            mat;
243   Mat_SeqAIJ     *gmata;
244   PetscMPIInt    tag;
245   MPI_Status     status;
246   PetscBool      aij;
247   MatScalar      *gmataa,*ao,*ad,*gmataarestore=0;
248 
249   PetscFunctionBegin;
250   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
251   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
252   if (!rank) {
253     ierr = PetscObjectTypeCompare((PetscObject)gmat,MATSEQAIJ,&aij);CHKERRQ(ierr);
254     if (!aij) SETERRQ1(PetscObjectComm((PetscObject)gmat),PETSC_ERR_SUP,"Currently no support for input matrix of type %s\n",((PetscObject)gmat)->type_name);
255   }
256   if (reuse == MAT_INITIAL_MATRIX) {
257     ierr = MatCreate(comm,&mat);CHKERRQ(ierr);
258     ierr = MatSetSizes(mat,m,m,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
259     ierr = MatGetBlockSizes(gmat,&bses[0],&bses[1]);CHKERRQ(ierr);
260     ierr = MPI_Bcast(bses,2,MPIU_INT,0,comm);CHKERRQ(ierr);
261     ierr = MatSetBlockSizes(mat,bses[0],bses[1]);CHKERRQ(ierr);
262     ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
263     ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
264     ierr = PetscMalloc2(m,&dlens,m,&olens);CHKERRQ(ierr);
265     ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
266 
267     rowners[0] = 0;
268     for (i=2; i<=size; i++) rowners[i] += rowners[i-1];
269     rstart = rowners[rank];
270     rend   = rowners[rank+1];
271     ierr   = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
272     if (!rank) {
273       gmata = (Mat_SeqAIJ*) gmat->data;
274       /* send row lengths to all processors */
275       for (i=0; i<m; i++) dlens[i] = gmata->ilen[i];
276       for (i=1; i<size; i++) {
277         ierr = MPI_Send(gmata->ilen + rowners[i],rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
278       }
279       /* determine number diagonal and off-diagonal counts */
280       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
281       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
282       jj   = 0;
283       for (i=0; i<m; i++) {
284         for (j=0; j<dlens[i]; j++) {
285           if (gmata->j[jj] < rstart) ld[i]++;
286           if (gmata->j[jj] < rstart || gmata->j[jj] >= rend) olens[i]++;
287           jj++;
288         }
289       }
290       /* send column indices to other processes */
291       for (i=1; i<size; i++) {
292         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
293         ierr = MPI_Send(&nz,1,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
294         ierr = MPI_Send(gmata->j + gmata->i[rowners[i]],nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
295       }
296 
297       /* send numerical values to other processes */
298       for (i=1; i<size; i++) {
299         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
300         ierr = MPI_Send(gmata->a + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
301       }
302       gmataa = gmata->a;
303       gmataj = gmata->j;
304 
305     } else {
306       /* receive row lengths */
307       ierr = MPI_Recv(dlens,m,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
308       /* receive column indices */
309       ierr = MPI_Recv(&nz,1,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
310       ierr = PetscMalloc2(nz,&gmataa,nz,&gmataj);CHKERRQ(ierr);
311       ierr = MPI_Recv(gmataj,nz,MPIU_INT,0,tag,comm,&status);CHKERRQ(ierr);
312       /* determine number diagonal and off-diagonal counts */
313       ierr = PetscMemzero(olens,m*sizeof(PetscInt));CHKERRQ(ierr);
314       ierr = PetscCalloc1(m,&ld);CHKERRQ(ierr);
315       jj   = 0;
316       for (i=0; i<m; i++) {
317         for (j=0; j<dlens[i]; j++) {
318           if (gmataj[jj] < rstart) ld[i]++;
319           if (gmataj[jj] < rstart || gmataj[jj] >= rend) olens[i]++;
320           jj++;
321         }
322       }
323       /* receive numerical values */
324       ierr = PetscMemzero(gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
325       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
326     }
327     /* set preallocation */
328     for (i=0; i<m; i++) {
329       dlens[i] -= olens[i];
330     }
331     ierr = MatSeqAIJSetPreallocation(mat,0,dlens);CHKERRQ(ierr);
332     ierr = MatMPIAIJSetPreallocation(mat,0,dlens,0,olens);CHKERRQ(ierr);
333 
334     for (i=0; i<m; i++) {
335       dlens[i] += olens[i];
336     }
337     cnt = 0;
338     for (i=0; i<m; i++) {
339       row  = rstart + i;
340       ierr = MatSetValues(mat,1,&row,dlens[i],gmataj+cnt,gmataa+cnt,INSERT_VALUES);CHKERRQ(ierr);
341       cnt += dlens[i];
342     }
343     if (rank) {
344       ierr = PetscFree2(gmataa,gmataj);CHKERRQ(ierr);
345     }
346     ierr = PetscFree2(dlens,olens);CHKERRQ(ierr);
347     ierr = PetscFree(rowners);CHKERRQ(ierr);
348 
349     ((Mat_MPIAIJ*)(mat->data))->ld = ld;
350 
351     *inmat = mat;
352   } else {   /* column indices are already set; only need to move over numerical values from process 0 */
353     Mat_SeqAIJ *Ad = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->A->data;
354     Mat_SeqAIJ *Ao = (Mat_SeqAIJ*)((Mat_MPIAIJ*)((*inmat)->data))->B->data;
355     mat  = *inmat;
356     ierr = PetscObjectGetNewTag((PetscObject)mat,&tag);CHKERRQ(ierr);
357     if (!rank) {
358       /* send numerical values to other processes */
359       gmata  = (Mat_SeqAIJ*) gmat->data;
360       ierr   = MatGetOwnershipRanges(mat,(const PetscInt**)&rowners);CHKERRQ(ierr);
361       gmataa = gmata->a;
362       for (i=1; i<size; i++) {
363         nz   = gmata->i[rowners[i+1]]-gmata->i[rowners[i]];
364         ierr = MPI_Send(gmataa + gmata->i[rowners[i]],nz,MPIU_SCALAR,i,tag,comm);CHKERRQ(ierr);
365       }
366       nz = gmata->i[rowners[1]]-gmata->i[rowners[0]];
367     } else {
368       /* receive numerical values from process 0*/
369       nz   = Ad->nz + Ao->nz;
370       ierr = PetscMalloc1(nz,&gmataa);CHKERRQ(ierr); gmataarestore = gmataa;
371       ierr = MPI_Recv(gmataa,nz,MPIU_SCALAR,0,tag,comm,&status);CHKERRQ(ierr);
372     }
373     /* transfer numerical values into the diagonal A and off diagonal B parts of mat */
374     ld = ((Mat_MPIAIJ*)(mat->data))->ld;
375     ad = Ad->a;
376     ao = Ao->a;
377     if (mat->rmap->n) {
378       i  = 0;
379       nz = ld[i];                                   ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
380       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
381     }
382     for (i=1; i<mat->rmap->n; i++) {
383       nz = Ao->i[i] - Ao->i[i-1] - ld[i-1] + ld[i]; ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ao += nz; gmataa += nz;
384       nz = Ad->i[i+1] - Ad->i[i];                   ierr = PetscMemcpy(ad,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr); ad += nz; gmataa += nz;
385     }
386     i--;
387     if (mat->rmap->n) {
388       nz = Ao->i[i+1] - Ao->i[i] - ld[i];           ierr = PetscMemcpy(ao,gmataa,nz*sizeof(PetscScalar));CHKERRQ(ierr);
389     }
390     if (rank) {
391       ierr = PetscFree(gmataarestore);CHKERRQ(ierr);
392     }
393   }
394   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
395   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
396   PetscFunctionReturn(0);
397 }
398 
399 /*
400   Local utility routine that creates a mapping from the global column
401 number to the local number in the off-diagonal part of the local
402 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
403 a slightly higher hash table cost; without it it is not scalable (each processor
404 has an order N integer array but is fast to acess.
405 */
406 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
407 {
408   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
409   PetscErrorCode ierr;
410   PetscInt       n = aij->B->cmap->n,i;
411 
412   PetscFunctionBegin;
413   if (!aij->garray) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MPIAIJ Matrix was assembled but is missing garray");
414 #if defined(PETSC_USE_CTABLE)
415   ierr = PetscTableCreate(n,mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
416   for (i=0; i<n; i++) {
417     ierr = PetscTableAdd(aij->colmap,aij->garray[i]+1,i+1,INSERT_VALUES);CHKERRQ(ierr);
418   }
419 #else
420   ierr = PetscCalloc1(mat->cmap->N+1,&aij->colmap);CHKERRQ(ierr);
421   ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N+1)*sizeof(PetscInt));CHKERRQ(ierr);
422   for (i=0; i<n; i++) aij->colmap[aij->garray[i]] = i+1;
423 #endif
424   PetscFunctionReturn(0);
425 }
426 
427 #define MatSetValues_SeqAIJ_A_Private(row,col,value,addv,orow,ocol)     \
428 { \
429     if (col <= lastcol1)  low1 = 0;     \
430     else                 high1 = nrow1; \
431     lastcol1 = col;\
432     while (high1-low1 > 5) { \
433       t = (low1+high1)/2; \
434       if (rp1[t] > col) high1 = t; \
435       else              low1  = t; \
436     } \
437       for (_i=low1; _i<high1; _i++) { \
438         if (rp1[_i] > col) break; \
439         if (rp1[_i] == col) { \
440           if (addv == ADD_VALUES) ap1[_i] += value;   \
441           else                    ap1[_i] = value; \
442           goto a_noinsert; \
443         } \
444       }  \
445       if (value == 0.0 && ignorezeroentries && row != col) {low1 = 0; high1 = nrow1;goto a_noinsert;} \
446       if (nonew == 1) {low1 = 0; high1 = nrow1; goto a_noinsert;}                \
447       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
448       MatSeqXAIJReallocateAIJ(A,am,1,nrow1,row,col,rmax1,aa,ai,aj,rp1,ap1,aimax,nonew,MatScalar); \
449       N = nrow1++ - 1; a->nz++; high1++; \
450       /* shift up all the later entries in this row */ \
451       for (ii=N; ii>=_i; ii--) { \
452         rp1[ii+1] = rp1[ii]; \
453         ap1[ii+1] = ap1[ii]; \
454       } \
455       rp1[_i] = col;  \
456       ap1[_i] = value;  \
457       A->nonzerostate++;\
458       a_noinsert: ; \
459       ailen[row] = nrow1; \
460 }
461 
462 
463 #define MatSetValues_SeqAIJ_B_Private(row,col,value,addv,orow,ocol) \
464   { \
465     if (col <= lastcol2) low2 = 0;                        \
466     else high2 = nrow2;                                   \
467     lastcol2 = col;                                       \
468     while (high2-low2 > 5) {                              \
469       t = (low2+high2)/2;                                 \
470       if (rp2[t] > col) high2 = t;                        \
471       else             low2  = t;                         \
472     }                                                     \
473     for (_i=low2; _i<high2; _i++) {                       \
474       if (rp2[_i] > col) break;                           \
475       if (rp2[_i] == col) {                               \
476         if (addv == ADD_VALUES) ap2[_i] += value;         \
477         else                    ap2[_i] = value;          \
478         goto b_noinsert;                                  \
479       }                                                   \
480     }                                                     \
481     if (value == 0.0 && ignorezeroentries) {low2 = 0; high2 = nrow2; goto b_noinsert;} \
482     if (nonew == 1) {low2 = 0; high2 = nrow2; goto b_noinsert;}                        \
483     if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", orow, ocol); \
484     MatSeqXAIJReallocateAIJ(B,bm,1,nrow2,row,col,rmax2,ba,bi,bj,rp2,ap2,bimax,nonew,MatScalar); \
485     N = nrow2++ - 1; b->nz++; high2++;                    \
486     /* shift up all the later entries in this row */      \
487     for (ii=N; ii>=_i; ii--) {                            \
488       rp2[ii+1] = rp2[ii];                                \
489       ap2[ii+1] = ap2[ii];                                \
490     }                                                     \
491     rp2[_i] = col;                                        \
492     ap2[_i] = value;                                      \
493     B->nonzerostate++;                                    \
494     b_noinsert: ;                                         \
495     bilen[row] = nrow2;                                   \
496   }
497 
498 PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A,PetscInt row,const PetscScalar v[])
499 {
500   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)A->data;
501   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)mat->A->data,*b = (Mat_SeqAIJ*)mat->B->data;
502   PetscErrorCode ierr;
503   PetscInt       l,*garray = mat->garray,diag;
504 
505   PetscFunctionBegin;
506   /* code only works for square matrices A */
507 
508   /* find size of row to the left of the diagonal part */
509   ierr = MatGetOwnershipRange(A,&diag,0);CHKERRQ(ierr);
510   row  = row - diag;
511   for (l=0; l<b->i[row+1]-b->i[row]; l++) {
512     if (garray[b->j[b->i[row]+l]] > diag) break;
513   }
514   ierr = PetscMemcpy(b->a+b->i[row],v,l*sizeof(PetscScalar));CHKERRQ(ierr);
515 
516   /* diagonal part */
517   ierr = PetscMemcpy(a->a+a->i[row],v+l,(a->i[row+1]-a->i[row])*sizeof(PetscScalar));CHKERRQ(ierr);
518 
519   /* right of diagonal part */
520   ierr = PetscMemcpy(b->a+b->i[row]+l,v+l+a->i[row+1]-a->i[row],(b->i[row+1]-b->i[row]-l)*sizeof(PetscScalar));CHKERRQ(ierr);
521   PetscFunctionReturn(0);
522 }
523 
524 PetscErrorCode MatSetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode addv)
525 {
526   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
527   PetscScalar    value;
528   PetscErrorCode ierr;
529   PetscInt       i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
530   PetscInt       cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
531   PetscBool      roworiented = aij->roworiented;
532 
533   /* Some Variables required in the macro */
534   Mat        A                 = aij->A;
535   Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
536   PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
537   MatScalar  *aa               = a->a;
538   PetscBool  ignorezeroentries = a->ignorezeroentries;
539   Mat        B                 = aij->B;
540   Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
541   PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
542   MatScalar  *ba               = b->a;
543 
544   PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
545   PetscInt  nonew;
546   MatScalar *ap1,*ap2;
547 
548   PetscFunctionBegin;
549   for (i=0; i<m; i++) {
550     if (im[i] < 0) continue;
551 #if defined(PETSC_USE_DEBUG)
552     if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
553 #endif
554     if (im[i] >= rstart && im[i] < rend) {
555       row      = im[i] - rstart;
556       lastcol1 = -1;
557       rp1      = aj + ai[row];
558       ap1      = aa + ai[row];
559       rmax1    = aimax[row];
560       nrow1    = ailen[row];
561       low1     = 0;
562       high1    = nrow1;
563       lastcol2 = -1;
564       rp2      = bj + bi[row];
565       ap2      = ba + bi[row];
566       rmax2    = bimax[row];
567       nrow2    = bilen[row];
568       low2     = 0;
569       high2    = nrow2;
570 
571       for (j=0; j<n; j++) {
572         if (roworiented) value = v[i*n+j];
573         else             value = v[i+j*m];
574         if (in[j] >= cstart && in[j] < cend) {
575           col   = in[j] - cstart;
576           nonew = a->nonew;
577           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
578           MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
579         } else if (in[j] < 0) continue;
580 #if defined(PETSC_USE_DEBUG)
581         else if (in[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);
582 #endif
583         else {
584           if (mat->was_assembled) {
585             if (!aij->colmap) {
586               ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
587             }
588 #if defined(PETSC_USE_CTABLE)
589             ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
590             col--;
591 #else
592             col = aij->colmap[in[j]] - 1;
593 #endif
594             if (col < 0 && !((Mat_SeqAIJ*)(aij->B->data))->nonew) {
595               ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
596               col  =  in[j];
597               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
598               B     = aij->B;
599               b     = (Mat_SeqAIJ*)B->data;
600               bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j; ba = b->a;
601               rp2   = bj + bi[row];
602               ap2   = ba + bi[row];
603               rmax2 = bimax[row];
604               nrow2 = bilen[row];
605               low2  = 0;
606               high2 = nrow2;
607               bm    = aij->B->rmap->n;
608               ba    = b->a;
609             } else if (col < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero at global row/column (%D, %D) into matrix", im[i], in[j]);
610           } else col = in[j];
611           nonew = b->nonew;
612           MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
613         }
614       }
615     } else {
616       if (mat->nooffprocentries) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Setting off process row %D even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set",im[i]);
617       if (!aij->donotstash) {
618         mat->assembled = PETSC_FALSE;
619         if (roworiented) {
620           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
621         } else {
622           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
623         }
624       }
625     }
626   }
627   PetscFunctionReturn(0);
628 }
629 
630 PetscErrorCode MatGetValues_MPIAIJ(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
631 {
632   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
633   PetscErrorCode ierr;
634   PetscInt       i,j,rstart = mat->rmap->rstart,rend = mat->rmap->rend;
635   PetscInt       cstart = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
636 
637   PetscFunctionBegin;
638   for (i=0; i<m; i++) {
639     if (idxm[i] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative row: %D",idxm[i]);*/
640     if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",idxm[i],mat->rmap->N-1);
641     if (idxm[i] >= rstart && idxm[i] < rend) {
642       row = idxm[i] - rstart;
643       for (j=0; j<n; j++) {
644         if (idxn[j] < 0) continue; /* SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative column: %D",idxn[j]); */
645         if (idxn[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",idxn[j],mat->cmap->N-1);
646         if (idxn[j] >= cstart && idxn[j] < cend) {
647           col  = idxn[j] - cstart;
648           ierr = MatGetValues(aij->A,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
649         } else {
650           if (!aij->colmap) {
651             ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
652           }
653 #if defined(PETSC_USE_CTABLE)
654           ierr = PetscTableFind(aij->colmap,idxn[j]+1,&col);CHKERRQ(ierr);
655           col--;
656 #else
657           col = aij->colmap[idxn[j]] - 1;
658 #endif
659           if ((col < 0) || (aij->garray[col] != idxn[j])) *(v+i*n+j) = 0.0;
660           else {
661             ierr = MatGetValues(aij->B,1,&row,1,&col,v+i*n+j);CHKERRQ(ierr);
662           }
663         }
664       }
665     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only local values currently supported");
666   }
667   PetscFunctionReturn(0);
668 }
669 
670 extern PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat,Vec,Vec);
671 
672 PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat,MatAssemblyType mode)
673 {
674   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
675   PetscErrorCode ierr;
676   PetscInt       nstash,reallocs;
677 
678   PetscFunctionBegin;
679   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(0);
680 
681   ierr = MatStashScatterBegin_Private(mat,&mat->stash,mat->rmap->range);CHKERRQ(ierr);
682   ierr = MatStashGetInfo_Private(&mat->stash,&nstash,&reallocs);CHKERRQ(ierr);
683   ierr = PetscInfo2(aij->A,"Stash has %D entries, uses %D mallocs.\n",nstash,reallocs);CHKERRQ(ierr);
684   PetscFunctionReturn(0);
685 }
686 
687 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat,MatAssemblyType mode)
688 {
689   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
690   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)aij->A->data;
691   PetscErrorCode ierr;
692   PetscMPIInt    n;
693   PetscInt       i,j,rstart,ncols,flg;
694   PetscInt       *row,*col;
695   PetscBool      other_disassembled;
696   PetscScalar    *val;
697 
698   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
699 
700   PetscFunctionBegin;
701   if (!aij->donotstash && !mat->nooffprocentries) {
702     while (1) {
703       ierr = MatStashScatterGetMesg_Private(&mat->stash,&n,&row,&col,&val,&flg);CHKERRQ(ierr);
704       if (!flg) break;
705 
706       for (i=0; i<n; ) {
707         /* Now identify the consecutive vals belonging to the same row */
708         for (j=i,rstart=row[j]; j<n; j++) {
709           if (row[j] != rstart) break;
710         }
711         if (j < n) ncols = j-i;
712         else       ncols = n-i;
713         /* Now assemble all these values with a single function call */
714         ierr = MatSetValues_MPIAIJ(mat,1,row+i,ncols,col+i,val+i,mat->insertmode);CHKERRQ(ierr);
715 
716         i = j;
717       }
718     }
719     ierr = MatStashScatterEnd_Private(&mat->stash);CHKERRQ(ierr);
720   }
721   ierr = MatAssemblyBegin(aij->A,mode);CHKERRQ(ierr);
722   ierr = MatAssemblyEnd(aij->A,mode);CHKERRQ(ierr);
723 
724   /* determine if any processor has disassembled, if so we must
725      also disassemble ourselfs, in order that we may reassemble. */
726   /*
727      if nonzero structure of submatrix B cannot change then we know that
728      no processor disassembled thus we can skip this stuff
729   */
730   if (!((Mat_SeqAIJ*)aij->B->data)->nonew) {
731     ierr = MPIU_Allreduce(&mat->was_assembled,&other_disassembled,1,MPIU_BOOL,MPI_PROD,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
732     if (mat->was_assembled && !other_disassembled) {
733       ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
734     }
735   }
736   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) {
737     ierr = MatSetUpMultiply_MPIAIJ(mat);CHKERRQ(ierr);
738   }
739   ierr = MatSetOption(aij->B,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
740   ierr = MatAssemblyBegin(aij->B,mode);CHKERRQ(ierr);
741   ierr = MatAssemblyEnd(aij->B,mode);CHKERRQ(ierr);
742 
743   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
744 
745   aij->rowvalues = 0;
746 
747   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
748   if (a->inode.size) mat->ops->multdiagonalblock = MatMultDiagonalBlock_MPIAIJ;
749 
750   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
751   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
752     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
753     ierr = MPIU_Allreduce(&state,&mat->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
754   }
755   PetscFunctionReturn(0);
756 }
757 
758 PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
759 {
760   Mat_MPIAIJ     *l = (Mat_MPIAIJ*)A->data;
761   PetscErrorCode ierr;
762 
763   PetscFunctionBegin;
764   ierr = MatZeroEntries(l->A);CHKERRQ(ierr);
765   ierr = MatZeroEntries(l->B);CHKERRQ(ierr);
766   PetscFunctionReturn(0);
767 }
768 
769 PetscErrorCode MatZeroRows_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
770 {
771   Mat_MPIAIJ    *mat    = (Mat_MPIAIJ *) A->data;
772   PetscInt      *lrows;
773   PetscInt       r, len;
774   PetscErrorCode ierr;
775 
776   PetscFunctionBegin;
777   /* get locally owned rows */
778   ierr = MatZeroRowsMapLocal_Private(A,N,rows,&len,&lrows);CHKERRQ(ierr);
779   /* fix right hand side if needed */
780   if (x && b) {
781     const PetscScalar *xx;
782     PetscScalar       *bb;
783 
784     ierr = VecGetArrayRead(x, &xx);CHKERRQ(ierr);
785     ierr = VecGetArray(b, &bb);CHKERRQ(ierr);
786     for (r = 0; r < len; ++r) bb[lrows[r]] = diag*xx[lrows[r]];
787     ierr = VecRestoreArrayRead(x, &xx);CHKERRQ(ierr);
788     ierr = VecRestoreArray(b, &bb);CHKERRQ(ierr);
789   }
790   /* Must zero l->B before l->A because the (diag) case below may put values into l->B*/
791   ierr = MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
792   if (A->congruentlayouts == -1) { /* first time we compare rows and cols layouts */
793     PetscBool cong;
794     ierr = PetscLayoutCompare(A->rmap,A->cmap,&cong);CHKERRQ(ierr);
795     if (cong) A->congruentlayouts = 1;
796     else      A->congruentlayouts = 0;
797   }
798   if ((diag != 0.0) && A->congruentlayouts) {
799     ierr = MatZeroRows(mat->A, len, lrows, diag, NULL, NULL);CHKERRQ(ierr);
800   } else if (diag != 0.0) {
801     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
802     if (((Mat_SeqAIJ *) mat->A->data)->nonew) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatZeroRows() on rectangular matrices cannot be used with the Mat options\nMAT_NEW_NONZERO_LOCATIONS,MAT_NEW_NONZERO_LOCATION_ERR,MAT_NEW_NONZERO_ALLOCATION_ERR");
803     for (r = 0; r < len; ++r) {
804       const PetscInt row = lrows[r] + A->rmap->rstart;
805       ierr = MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES);CHKERRQ(ierr);
806     }
807     ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
808     ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
809   } else {
810     ierr = MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL);CHKERRQ(ierr);
811   }
812   ierr = PetscFree(lrows);CHKERRQ(ierr);
813 
814   /* only change matrix nonzero state if pattern was allowed to be changed */
815   if (!((Mat_SeqAIJ*)(mat->A->data))->keepnonzeropattern) {
816     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
817     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
818   }
819   PetscFunctionReturn(0);
820 }
821 
822 PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A,PetscInt N,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
823 {
824   Mat_MPIAIJ        *l = (Mat_MPIAIJ*)A->data;
825   PetscErrorCode    ierr;
826   PetscMPIInt       n = A->rmap->n;
827   PetscInt          i,j,r,m,p = 0,len = 0;
828   PetscInt          *lrows,*owners = A->rmap->range;
829   PetscSFNode       *rrows;
830   PetscSF           sf;
831   const PetscScalar *xx;
832   PetscScalar       *bb,*mask;
833   Vec               xmask,lmask;
834   Mat_SeqAIJ        *aij = (Mat_SeqAIJ*)l->B->data;
835   const PetscInt    *aj, *ii,*ridx;
836   PetscScalar       *aa;
837 
838   PetscFunctionBegin;
839   /* Create SF where leaves are input rows and roots are owned rows */
840   ierr = PetscMalloc1(n, &lrows);CHKERRQ(ierr);
841   for (r = 0; r < n; ++r) lrows[r] = -1;
842   ierr = PetscMalloc1(N, &rrows);CHKERRQ(ierr);
843   for (r = 0; r < N; ++r) {
844     const PetscInt idx   = rows[r];
845     if (idx < 0 || A->rmap->N <= idx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row %D out of range [0,%D)",idx,A->rmap->N);
846     if (idx < owners[p] || owners[p+1] <= idx) { /* short-circuit the search if the last p owns this row too */
847       ierr = PetscLayoutFindOwner(A->rmap,idx,&p);CHKERRQ(ierr);
848     }
849     rrows[r].rank  = p;
850     rrows[r].index = rows[r] - owners[p];
851   }
852   ierr = PetscSFCreate(PetscObjectComm((PetscObject) A), &sf);CHKERRQ(ierr);
853   ierr = PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER);CHKERRQ(ierr);
854   /* Collect flags for rows to be zeroed */
855   ierr = PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
856   ierr = PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *) rows, lrows, MPI_LOR);CHKERRQ(ierr);
857   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
858   /* Compress and put in row numbers */
859   for (r = 0; r < n; ++r) if (lrows[r] >= 0) lrows[len++] = r;
860   /* zero diagonal part of matrix */
861   ierr = MatZeroRowsColumns(l->A,len,lrows,diag,x,b);CHKERRQ(ierr);
862   /* handle off diagonal part of matrix */
863   ierr = MatCreateVecs(A,&xmask,NULL);CHKERRQ(ierr);
864   ierr = VecDuplicate(l->lvec,&lmask);CHKERRQ(ierr);
865   ierr = VecGetArray(xmask,&bb);CHKERRQ(ierr);
866   for (i=0; i<len; i++) bb[lrows[i]] = 1;
867   ierr = VecRestoreArray(xmask,&bb);CHKERRQ(ierr);
868   ierr = VecScatterBegin(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
869   ierr = VecScatterEnd(l->Mvctx,xmask,lmask,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
870   ierr = VecDestroy(&xmask);CHKERRQ(ierr);
871   if (x) {
872     ierr = VecScatterBegin(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
873     ierr = VecScatterEnd(l->Mvctx,x,l->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
874     ierr = VecGetArrayRead(l->lvec,&xx);CHKERRQ(ierr);
875     ierr = VecGetArray(b,&bb);CHKERRQ(ierr);
876   }
877   ierr = VecGetArray(lmask,&mask);CHKERRQ(ierr);
878   /* remove zeroed rows of off diagonal matrix */
879   ii = aij->i;
880   for (i=0; i<len; i++) {
881     ierr = PetscMemzero(aij->a + ii[lrows[i]],(ii[lrows[i]+1] - ii[lrows[i]])*sizeof(PetscScalar));CHKERRQ(ierr);
882   }
883   /* loop over all elements of off process part of matrix zeroing removed columns*/
884   if (aij->compressedrow.use) {
885     m    = aij->compressedrow.nrows;
886     ii   = aij->compressedrow.i;
887     ridx = aij->compressedrow.rindex;
888     for (i=0; i<m; i++) {
889       n  = ii[i+1] - ii[i];
890       aj = aij->j + ii[i];
891       aa = aij->a + ii[i];
892 
893       for (j=0; j<n; j++) {
894         if (PetscAbsScalar(mask[*aj])) {
895           if (b) bb[*ridx] -= *aa*xx[*aj];
896           *aa = 0.0;
897         }
898         aa++;
899         aj++;
900       }
901       ridx++;
902     }
903   } else { /* do not use compressed row format */
904     m = l->B->rmap->n;
905     for (i=0; i<m; i++) {
906       n  = ii[i+1] - ii[i];
907       aj = aij->j + ii[i];
908       aa = aij->a + ii[i];
909       for (j=0; j<n; j++) {
910         if (PetscAbsScalar(mask[*aj])) {
911           if (b) bb[i] -= *aa*xx[*aj];
912           *aa = 0.0;
913         }
914         aa++;
915         aj++;
916       }
917     }
918   }
919   if (x) {
920     ierr = VecRestoreArray(b,&bb);CHKERRQ(ierr);
921     ierr = VecRestoreArrayRead(l->lvec,&xx);CHKERRQ(ierr);
922   }
923   ierr = VecRestoreArray(lmask,&mask);CHKERRQ(ierr);
924   ierr = VecDestroy(&lmask);CHKERRQ(ierr);
925   ierr = PetscFree(lrows);CHKERRQ(ierr);
926 
927   /* only change matrix nonzero state if pattern was allowed to be changed */
928   if (!((Mat_SeqAIJ*)(l->A->data))->keepnonzeropattern) {
929     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
930     ierr = MPIU_Allreduce(&state,&A->nonzerostate,1,MPIU_INT64,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
931   }
932   PetscFunctionReturn(0);
933 }
934 
935 PetscErrorCode MatMult_MPIAIJ(Mat A,Vec xx,Vec yy)
936 {
937   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
938   PetscErrorCode ierr;
939   PetscInt       nt;
940 
941   PetscFunctionBegin;
942   ierr = VecGetLocalSize(xx,&nt);CHKERRQ(ierr);
943   if (nt != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible partition of A (%D) and xx (%D)",A->cmap->n,nt);
944   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
945   ierr = (*a->A->ops->mult)(a->A,xx,yy);CHKERRQ(ierr);
946   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
947   ierr = (*a->B->ops->multadd)(a->B,a->lvec,yy,yy);CHKERRQ(ierr);
948   PetscFunctionReturn(0);
949 }
950 
951 PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A,Vec bb,Vec xx)
952 {
953   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
954   PetscErrorCode ierr;
955 
956   PetscFunctionBegin;
957   ierr = MatMultDiagonalBlock(a->A,bb,xx);CHKERRQ(ierr);
958   PetscFunctionReturn(0);
959 }
960 
961 PetscErrorCode MatMultAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
962 {
963   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
964   PetscErrorCode ierr;
965 
966   PetscFunctionBegin;
967   ierr = VecScatterBegin(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
968   ierr = (*a->A->ops->multadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
969   ierr = VecScatterEnd(a->Mvctx,xx,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
970   ierr = (*a->B->ops->multadd)(a->B,a->lvec,zz,zz);CHKERRQ(ierr);
971   PetscFunctionReturn(0);
972 }
973 
974 PetscErrorCode MatMultTranspose_MPIAIJ(Mat A,Vec xx,Vec yy)
975 {
976   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
977   PetscErrorCode ierr;
978   PetscBool      merged;
979 
980   PetscFunctionBegin;
981   ierr = VecScatterGetMerged(a->Mvctx,&merged);CHKERRQ(ierr);
982   /* do nondiagonal part */
983   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
984   if (!merged) {
985     /* send it on its way */
986     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
987     /* do local part */
988     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
989     /* receive remote parts: note this assumes the values are not actually */
990     /* added in yy until the next line, */
991     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
992   } else {
993     /* do local part */
994     ierr = (*a->A->ops->multtranspose)(a->A,xx,yy);CHKERRQ(ierr);
995     /* send it on its way */
996     ierr = VecScatterBegin(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
997     /* values actually were received in the Begin() but we need to call this nop */
998     ierr = VecScatterEnd(a->Mvctx,a->lvec,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
999   }
1000   PetscFunctionReturn(0);
1001 }
1002 
1003 PetscErrorCode  MatIsTranspose_MPIAIJ(Mat Amat,Mat Bmat,PetscReal tol,PetscBool  *f)
1004 {
1005   MPI_Comm       comm;
1006   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ*) Amat->data, *Bij;
1007   Mat            Adia = Aij->A, Bdia, Aoff,Boff,*Aoffs,*Boffs;
1008   IS             Me,Notme;
1009   PetscErrorCode ierr;
1010   PetscInt       M,N,first,last,*notme,i;
1011   PetscMPIInt    size;
1012 
1013   PetscFunctionBegin;
1014   /* Easy test: symmetric diagonal block */
1015   Bij  = (Mat_MPIAIJ*) Bmat->data; Bdia = Bij->A;
1016   ierr = MatIsTranspose(Adia,Bdia,tol,f);CHKERRQ(ierr);
1017   if (!*f) PetscFunctionReturn(0);
1018   ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ(ierr);
1019   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
1020   if (size == 1) PetscFunctionReturn(0);
1021 
1022   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1023   ierr = MatGetSize(Amat,&M,&N);CHKERRQ(ierr);
1024   ierr = MatGetOwnershipRange(Amat,&first,&last);CHKERRQ(ierr);
1025   ierr = PetscMalloc1(N-last+first,&notme);CHKERRQ(ierr);
1026   for (i=0; i<first; i++) notme[i] = i;
1027   for (i=last; i<M; i++) notme[i-last+first] = i;
1028   ierr = ISCreateGeneral(MPI_COMM_SELF,N-last+first,notme,PETSC_COPY_VALUES,&Notme);CHKERRQ(ierr);
1029   ierr = ISCreateStride(MPI_COMM_SELF,last-first,first,1,&Me);CHKERRQ(ierr);
1030   ierr = MatCreateSubMatrices(Amat,1,&Me,&Notme,MAT_INITIAL_MATRIX,&Aoffs);CHKERRQ(ierr);
1031   Aoff = Aoffs[0];
1032   ierr = MatCreateSubMatrices(Bmat,1,&Notme,&Me,MAT_INITIAL_MATRIX,&Boffs);CHKERRQ(ierr);
1033   Boff = Boffs[0];
1034   ierr = MatIsTranspose(Aoff,Boff,tol,f);CHKERRQ(ierr);
1035   ierr = MatDestroyMatrices(1,&Aoffs);CHKERRQ(ierr);
1036   ierr = MatDestroyMatrices(1,&Boffs);CHKERRQ(ierr);
1037   ierr = ISDestroy(&Me);CHKERRQ(ierr);
1038   ierr = ISDestroy(&Notme);CHKERRQ(ierr);
1039   ierr = PetscFree(notme);CHKERRQ(ierr);
1040   PetscFunctionReturn(0);
1041 }
1042 
1043 PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A,Vec xx,Vec yy,Vec zz)
1044 {
1045   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1046   PetscErrorCode ierr;
1047 
1048   PetscFunctionBegin;
1049   /* do nondiagonal part */
1050   ierr = (*a->B->ops->multtranspose)(a->B,xx,a->lvec);CHKERRQ(ierr);
1051   /* send it on its way */
1052   ierr = VecScatterBegin(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1053   /* do local part */
1054   ierr = (*a->A->ops->multtransposeadd)(a->A,xx,yy,zz);CHKERRQ(ierr);
1055   /* receive remote parts */
1056   ierr = VecScatterEnd(a->Mvctx,a->lvec,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
1057   PetscFunctionReturn(0);
1058 }
1059 
1060 /*
1061   This only works correctly for square matrices where the subblock A->A is the
1062    diagonal block
1063 */
1064 PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A,Vec v)
1065 {
1066   PetscErrorCode ierr;
1067   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1068 
1069   PetscFunctionBegin;
1070   if (A->rmap->N != A->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Supports only square matrix where A->A is diag block");
1071   if (A->rmap->rstart != A->cmap->rstart || A->rmap->rend != A->cmap->rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"row partition must equal col partition");
1072   ierr = MatGetDiagonal(a->A,v);CHKERRQ(ierr);
1073   PetscFunctionReturn(0);
1074 }
1075 
1076 PetscErrorCode MatScale_MPIAIJ(Mat A,PetscScalar aa)
1077 {
1078   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1079   PetscErrorCode ierr;
1080 
1081   PetscFunctionBegin;
1082   ierr = MatScale(a->A,aa);CHKERRQ(ierr);
1083   ierr = MatScale(a->B,aa);CHKERRQ(ierr);
1084   PetscFunctionReturn(0);
1085 }
1086 
1087 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
1088 {
1089   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1090   PetscErrorCode ierr;
1091 
1092   PetscFunctionBegin;
1093 #if defined(PETSC_USE_LOG)
1094   PetscLogObjectState((PetscObject)mat,"Rows=%D, Cols=%D",mat->rmap->N,mat->cmap->N);
1095 #endif
1096   ierr = MatStashDestroy_Private(&mat->stash);CHKERRQ(ierr);
1097   ierr = VecDestroy(&aij->diag);CHKERRQ(ierr);
1098   ierr = MatDestroy(&aij->A);CHKERRQ(ierr);
1099   ierr = MatDestroy(&aij->B);CHKERRQ(ierr);
1100 #if defined(PETSC_USE_CTABLE)
1101   ierr = PetscTableDestroy(&aij->colmap);CHKERRQ(ierr);
1102 #else
1103   ierr = PetscFree(aij->colmap);CHKERRQ(ierr);
1104 #endif
1105   ierr = PetscFree(aij->garray);CHKERRQ(ierr);
1106   ierr = VecDestroy(&aij->lvec);CHKERRQ(ierr);
1107   ierr = VecScatterDestroy(&aij->Mvctx);CHKERRQ(ierr);
1108   ierr = PetscFree2(aij->rowvalues,aij->rowindices);CHKERRQ(ierr);
1109   ierr = PetscFree(aij->ld);CHKERRQ(ierr);
1110   ierr = PetscFree(mat->data);CHKERRQ(ierr);
1111 
1112   ierr = PetscObjectChangeTypeName((PetscObject)mat,0);CHKERRQ(ierr);
1113   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatStoreValues_C",NULL);CHKERRQ(ierr);
1114   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatRetrieveValues_C",NULL);CHKERRQ(ierr);
1115   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatIsTranspose_C",NULL);CHKERRQ(ierr);
1116   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocation_C",NULL);CHKERRQ(ierr);
1117   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMPIAIJSetPreallocationCSR_C",NULL);CHKERRQ(ierr);
1118   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatDiagonalScaleLocal_C",NULL);CHKERRQ(ierr);
1119   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_mpisbaij_C",NULL);CHKERRQ(ierr);
1120 #if defined(PETSC_HAVE_ELEMENTAL)
1121   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_elemental_C",NULL);CHKERRQ(ierr);
1122 #endif
1123 #if defined(PETSC_HAVE_HYPRE)
1124   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatConvert_mpiaij_hypre_C",NULL);CHKERRQ(ierr);
1125   ierr = PetscObjectComposeFunction((PetscObject)mat,"MatMatMatMult_transpose_mpiaij_mpiaij_C",NULL);CHKERRQ(ierr);
1126 #endif
1127   PetscFunctionReturn(0);
1128 }
1129 
1130 PetscErrorCode MatView_MPIAIJ_Binary(Mat mat,PetscViewer viewer)
1131 {
1132   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1133   Mat_SeqAIJ     *A   = (Mat_SeqAIJ*)aij->A->data;
1134   Mat_SeqAIJ     *B   = (Mat_SeqAIJ*)aij->B->data;
1135   PetscErrorCode ierr;
1136   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
1137   int            fd;
1138   PetscInt       nz,header[4],*row_lengths,*range=0,rlen,i;
1139   PetscInt       nzmax,*column_indices,j,k,col,*garray = aij->garray,cnt,cstart = mat->cmap->rstart,rnz = 0;
1140   PetscScalar    *column_values;
1141   PetscInt       message_count,flowcontrolcount;
1142   FILE           *file;
1143 
1144   PetscFunctionBegin;
1145   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1146   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
1147   nz   = A->nz + B->nz;
1148   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
1149   if (!rank) {
1150     header[0] = MAT_FILE_CLASSID;
1151     header[1] = mat->rmap->N;
1152     header[2] = mat->cmap->N;
1153 
1154     ierr = MPI_Reduce(&nz,&header[3],1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1155     ierr = PetscBinaryWrite(fd,header,4,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1156     /* get largest number of rows any processor has */
1157     rlen  = mat->rmap->n;
1158     range = mat->rmap->range;
1159     for (i=1; i<size; i++) rlen = PetscMax(rlen,range[i+1] - range[i]);
1160   } else {
1161     ierr = MPI_Reduce(&nz,0,1,MPIU_INT,MPI_SUM,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1162     rlen = mat->rmap->n;
1163   }
1164 
1165   /* load up the local row counts */
1166   ierr = PetscMalloc1(rlen+1,&row_lengths);CHKERRQ(ierr);
1167   for (i=0; i<mat->rmap->n; i++) row_lengths[i] = A->i[i+1] - A->i[i] + B->i[i+1] - B->i[i];
1168 
1169   /* store the row lengths to the file */
1170   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1171   if (!rank) {
1172     ierr = PetscBinaryWrite(fd,row_lengths,mat->rmap->n,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1173     for (i=1; i<size; i++) {
1174       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1175       rlen = range[i+1] - range[i];
1176       ierr = MPIULong_Recv(row_lengths,rlen,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1177       ierr = PetscBinaryWrite(fd,row_lengths,rlen,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1178     }
1179     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1180   } else {
1181     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1182     ierr = MPIULong_Send(row_lengths,mat->rmap->n,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1183     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1184   }
1185   ierr = PetscFree(row_lengths);CHKERRQ(ierr);
1186 
1187   /* load up the local column indices */
1188   nzmax = nz; /* th processor needs space a largest processor needs */
1189   ierr  = MPI_Reduce(&nz,&nzmax,1,MPIU_INT,MPI_MAX,0,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1190   ierr  = PetscMalloc1(nzmax+1,&column_indices);CHKERRQ(ierr);
1191   cnt   = 0;
1192   for (i=0; i<mat->rmap->n; i++) {
1193     for (j=B->i[i]; j<B->i[i+1]; j++) {
1194       if ((col = garray[B->j[j]]) > cstart) break;
1195       column_indices[cnt++] = col;
1196     }
1197     for (k=A->i[i]; k<A->i[i+1]; k++) column_indices[cnt++] = A->j[k] + cstart;
1198     for (; j<B->i[i+1]; j++) column_indices[cnt++] = garray[B->j[j]];
1199   }
1200   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1201 
1202   /* store the column indices to the file */
1203   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1204   if (!rank) {
1205     MPI_Status status;
1206     ierr = PetscBinaryWrite(fd,column_indices,nz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1207     for (i=1; i<size; i++) {
1208       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1209       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1210       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1211       ierr = MPIULong_Recv(column_indices,rnz,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1212       ierr = PetscBinaryWrite(fd,column_indices,rnz,PETSC_INT,PETSC_TRUE);CHKERRQ(ierr);
1213     }
1214     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1215   } else {
1216     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1217     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1218     ierr = MPIULong_Send(column_indices,nz,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1219     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1220   }
1221   ierr = PetscFree(column_indices);CHKERRQ(ierr);
1222 
1223   /* load up the local column values */
1224   ierr = PetscMalloc1(nzmax+1,&column_values);CHKERRQ(ierr);
1225   cnt  = 0;
1226   for (i=0; i<mat->rmap->n; i++) {
1227     for (j=B->i[i]; j<B->i[i+1]; j++) {
1228       if (garray[B->j[j]] > cstart) break;
1229       column_values[cnt++] = B->a[j];
1230     }
1231     for (k=A->i[i]; k<A->i[i+1]; k++) column_values[cnt++] = A->a[k];
1232     for (; j<B->i[i+1]; j++) column_values[cnt++] = B->a[j];
1233   }
1234   if (cnt != A->nz + B->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Internal PETSc error: cnt = %D nz = %D",cnt,A->nz+B->nz);
1235 
1236   /* store the column values to the file */
1237   ierr = PetscViewerFlowControlStart(viewer,&message_count,&flowcontrolcount);CHKERRQ(ierr);
1238   if (!rank) {
1239     MPI_Status status;
1240     ierr = PetscBinaryWrite(fd,column_values,nz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1241     for (i=1; i<size; i++) {
1242       ierr = PetscViewerFlowControlStepMaster(viewer,i,&message_count,flowcontrolcount);CHKERRQ(ierr);
1243       ierr = MPI_Recv(&rnz,1,MPIU_INT,i,tag,PetscObjectComm((PetscObject)mat),&status);CHKERRQ(ierr);
1244       if (rnz > nzmax) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_LIB,"Internal PETSc error: nz = %D nzmax = %D",nz,nzmax);
1245       ierr = MPIULong_Recv(column_values,rnz,MPIU_SCALAR,i,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1246       ierr = PetscBinaryWrite(fd,column_values,rnz,PETSC_SCALAR,PETSC_TRUE);CHKERRQ(ierr);
1247     }
1248     ierr = PetscViewerFlowControlEndMaster(viewer,&message_count);CHKERRQ(ierr);
1249   } else {
1250     ierr = PetscViewerFlowControlStepWorker(viewer,rank,&message_count);CHKERRQ(ierr);
1251     ierr = MPI_Send(&nz,1,MPIU_INT,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1252     ierr = MPIULong_Send(column_values,nz,MPIU_SCALAR,0,tag,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1253     ierr = PetscViewerFlowControlEndWorker(viewer,&message_count);CHKERRQ(ierr);
1254   }
1255   ierr = PetscFree(column_values);CHKERRQ(ierr);
1256 
1257   ierr = PetscViewerBinaryGetInfoPointer(viewer,&file);CHKERRQ(ierr);
1258   if (file) fprintf(file,"-matload_block_size %d\n",(int)PetscAbs(mat->rmap->bs));
1259   PetscFunctionReturn(0);
1260 }
1261 
1262 #include <petscdraw.h>
1263 PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat,PetscViewer viewer)
1264 {
1265   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)mat->data;
1266   PetscErrorCode    ierr;
1267   PetscMPIInt       rank = aij->rank,size = aij->size;
1268   PetscBool         isdraw,iascii,isbinary;
1269   PetscViewer       sviewer;
1270   PetscViewerFormat format;
1271 
1272   PetscFunctionBegin;
1273   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1274   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1275   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1276   if (iascii) {
1277     ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
1278     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1279       MatInfo   info;
1280       PetscBool inodes;
1281 
1282       ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)mat),&rank);CHKERRQ(ierr);
1283       ierr = MatGetInfo(mat,MAT_LOCAL,&info);CHKERRQ(ierr);
1284       ierr = MatInodeGetInodeSizes(aij->A,NULL,(PetscInt**)&inodes,NULL);CHKERRQ(ierr);
1285       ierr = PetscViewerASCIIPushSynchronized(viewer);CHKERRQ(ierr);
1286       if (!inodes) {
1287         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, not using I-node routines\n",
1288                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1289       } else {
1290         ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] Local rows %D nz %D nz alloced %D mem %D, using I-node routines\n",
1291                                                   rank,mat->rmap->n,(PetscInt)info.nz_used,(PetscInt)info.nz_allocated,(PetscInt)info.memory);CHKERRQ(ierr);
1292       }
1293       ierr = MatGetInfo(aij->A,MAT_LOCAL,&info);CHKERRQ(ierr);
1294       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] on-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1295       ierr = MatGetInfo(aij->B,MAT_LOCAL,&info);CHKERRQ(ierr);
1296       ierr = PetscViewerASCIISynchronizedPrintf(viewer,"[%d] off-diagonal part: nz %D \n",rank,(PetscInt)info.nz_used);CHKERRQ(ierr);
1297       ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1298       ierr = PetscViewerASCIIPopSynchronized(viewer);CHKERRQ(ierr);
1299       ierr = PetscViewerASCIIPrintf(viewer,"Information on VecScatter used in matrix-vector product: \n");CHKERRQ(ierr);
1300       ierr = VecScatterView(aij->Mvctx,viewer);CHKERRQ(ierr);
1301       PetscFunctionReturn(0);
1302     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1303       PetscInt inodecount,inodelimit,*inodes;
1304       ierr = MatInodeGetInodeSizes(aij->A,&inodecount,&inodes,&inodelimit);CHKERRQ(ierr);
1305       if (inodes) {
1306         ierr = PetscViewerASCIIPrintf(viewer,"using I-node (on process 0) routines: found %D nodes, limit used is %D\n",inodecount,inodelimit);CHKERRQ(ierr);
1307       } else {
1308         ierr = PetscViewerASCIIPrintf(viewer,"not using I-node (on process 0) routines\n");CHKERRQ(ierr);
1309       }
1310       PetscFunctionReturn(0);
1311     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1312       PetscFunctionReturn(0);
1313     }
1314   } else if (isbinary) {
1315     if (size == 1) {
1316       ierr = PetscObjectSetName((PetscObject)aij->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1317       ierr = MatView(aij->A,viewer);CHKERRQ(ierr);
1318     } else {
1319       ierr = MatView_MPIAIJ_Binary(mat,viewer);CHKERRQ(ierr);
1320     }
1321     PetscFunctionReturn(0);
1322   } else if (isdraw) {
1323     PetscDraw draw;
1324     PetscBool isnull;
1325     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
1326     ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr);
1327     if (isnull) PetscFunctionReturn(0);
1328   }
1329 
1330   {
1331     /* assemble the entire matrix onto first processor. */
1332     Mat        A;
1333     Mat_SeqAIJ *Aloc;
1334     PetscInt   M = mat->rmap->N,N = mat->cmap->N,m,*ai,*aj,row,*cols,i,*ct;
1335     MatScalar  *a;
1336 
1337     ierr = MatCreate(PetscObjectComm((PetscObject)mat),&A);CHKERRQ(ierr);
1338     if (!rank) {
1339       ierr = MatSetSizes(A,M,N,M,N);CHKERRQ(ierr);
1340     } else {
1341       ierr = MatSetSizes(A,0,0,M,N);CHKERRQ(ierr);
1342     }
1343     /* This is just a temporary matrix, so explicitly using MATMPIAIJ is probably best */
1344     ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
1345     ierr = MatMPIAIJSetPreallocation(A,0,NULL,0,NULL);CHKERRQ(ierr);
1346     ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
1347     ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)A);CHKERRQ(ierr);
1348 
1349     /* copy over the A part */
1350     Aloc = (Mat_SeqAIJ*)aij->A->data;
1351     m    = aij->A->rmap->n; ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1352     row  = mat->rmap->rstart;
1353     for (i=0; i<ai[m]; i++) aj[i] += mat->cmap->rstart;
1354     for (i=0; i<m; i++) {
1355       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],aj,a,INSERT_VALUES);CHKERRQ(ierr);
1356       row++;
1357       a += ai[i+1]-ai[i]; aj += ai[i+1]-ai[i];
1358     }
1359     aj = Aloc->j;
1360     for (i=0; i<ai[m]; i++) aj[i] -= mat->cmap->rstart;
1361 
1362     /* copy over the B part */
1363     Aloc = (Mat_SeqAIJ*)aij->B->data;
1364     m    = aij->B->rmap->n;  ai = Aloc->i; aj = Aloc->j; a = Aloc->a;
1365     row  = mat->rmap->rstart;
1366     ierr = PetscMalloc1(ai[m]+1,&cols);CHKERRQ(ierr);
1367     ct   = cols;
1368     for (i=0; i<ai[m]; i++) cols[i] = aij->garray[aj[i]];
1369     for (i=0; i<m; i++) {
1370       ierr = MatSetValues(A,1,&row,ai[i+1]-ai[i],cols,a,INSERT_VALUES);CHKERRQ(ierr);
1371       row++;
1372       a += ai[i+1]-ai[i]; cols += ai[i+1]-ai[i];
1373     }
1374     ierr = PetscFree(ct);CHKERRQ(ierr);
1375     ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1376     ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1377     /*
1378        Everyone has to call to draw the matrix since the graphics waits are
1379        synchronized across all processors that share the PetscDraw object
1380     */
1381     ierr = PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1382     if (!rank) {
1383       ierr = PetscObjectSetName((PetscObject)((Mat_MPIAIJ*)(A->data))->A,((PetscObject)mat)->name);CHKERRQ(ierr);
1384       ierr = MatView_SeqAIJ(((Mat_MPIAIJ*)(A->data))->A,sviewer);CHKERRQ(ierr);
1385     }
1386     ierr = PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);CHKERRQ(ierr);
1387     ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
1388     ierr = MatDestroy(&A);CHKERRQ(ierr);
1389   }
1390   PetscFunctionReturn(0);
1391 }
1392 
1393 PetscErrorCode MatView_MPIAIJ(Mat mat,PetscViewer viewer)
1394 {
1395   PetscErrorCode ierr;
1396   PetscBool      iascii,isdraw,issocket,isbinary;
1397 
1398   PetscFunctionBegin;
1399   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
1400   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
1401   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
1402   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSOCKET,&issocket);CHKERRQ(ierr);
1403   if (iascii || isdraw || isbinary || issocket) {
1404     ierr = MatView_MPIAIJ_ASCIIorDraworSocket(mat,viewer);CHKERRQ(ierr);
1405   }
1406   PetscFunctionReturn(0);
1407 }
1408 
1409 PetscErrorCode MatSOR_MPIAIJ(Mat matin,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
1410 {
1411   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1412   PetscErrorCode ierr;
1413   Vec            bb1 = 0;
1414   PetscBool      hasop;
1415 
1416   PetscFunctionBegin;
1417   if (flag == SOR_APPLY_UPPER) {
1418     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1419     PetscFunctionReturn(0);
1420   }
1421 
1422   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) {
1423     ierr = VecDuplicate(bb,&bb1);CHKERRQ(ierr);
1424   }
1425 
1426   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1427     if (flag & SOR_ZERO_INITIAL_GUESS) {
1428       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1429       its--;
1430     }
1431 
1432     while (its--) {
1433       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1434       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1435 
1436       /* update rhs: bb1 = bb - B*x */
1437       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1438       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1439 
1440       /* local sweep */
1441       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_SYMMETRIC_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1442     }
1443   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1444     if (flag & SOR_ZERO_INITIAL_GUESS) {
1445       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1446       its--;
1447     }
1448     while (its--) {
1449       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1450       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1451 
1452       /* update rhs: bb1 = bb - B*x */
1453       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1454       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1455 
1456       /* local sweep */
1457       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_FORWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1458     }
1459   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1460     if (flag & SOR_ZERO_INITIAL_GUESS) {
1461       ierr = (*mat->A->ops->sor)(mat->A,bb,omega,flag,fshift,lits,1,xx);CHKERRQ(ierr);
1462       its--;
1463     }
1464     while (its--) {
1465       ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1466       ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1467 
1468       /* update rhs: bb1 = bb - B*x */
1469       ierr = VecScale(mat->lvec,-1.0);CHKERRQ(ierr);
1470       ierr = (*mat->B->ops->multadd)(mat->B,mat->lvec,bb,bb1);CHKERRQ(ierr);
1471 
1472       /* local sweep */
1473       ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,SOR_BACKWARD_SWEEP,fshift,lits,1,xx);CHKERRQ(ierr);
1474     }
1475   } else if (flag & SOR_EISENSTAT) {
1476     Vec xx1;
1477 
1478     ierr = VecDuplicate(bb,&xx1);CHKERRQ(ierr);
1479     ierr = (*mat->A->ops->sor)(mat->A,bb,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP),fshift,lits,1,xx);CHKERRQ(ierr);
1480 
1481     ierr = VecScatterBegin(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1482     ierr = VecScatterEnd(mat->Mvctx,xx,mat->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1483     if (!mat->diag) {
1484       ierr = MatCreateVecs(matin,&mat->diag,NULL);CHKERRQ(ierr);
1485       ierr = MatGetDiagonal(matin,mat->diag);CHKERRQ(ierr);
1486     }
1487     ierr = MatHasOperation(matin,MATOP_MULT_DIAGONAL_BLOCK,&hasop);CHKERRQ(ierr);
1488     if (hasop) {
1489       ierr = MatMultDiagonalBlock(matin,xx,bb1);CHKERRQ(ierr);
1490     } else {
1491       ierr = VecPointwiseMult(bb1,mat->diag,xx);CHKERRQ(ierr);
1492     }
1493     ierr = VecAYPX(bb1,(omega-2.0)/omega,bb);CHKERRQ(ierr);
1494 
1495     ierr = MatMultAdd(mat->B,mat->lvec,bb1,bb1);CHKERRQ(ierr);
1496 
1497     /* local sweep */
1498     ierr = (*mat->A->ops->sor)(mat->A,bb1,omega,(MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP),fshift,lits,1,xx1);CHKERRQ(ierr);
1499     ierr = VecAXPY(xx,1.0,xx1);CHKERRQ(ierr);
1500     ierr = VecDestroy(&xx1);CHKERRQ(ierr);
1501   } else SETERRQ(PetscObjectComm((PetscObject)matin),PETSC_ERR_SUP,"Parallel SOR not supported");
1502 
1503   ierr = VecDestroy(&bb1);CHKERRQ(ierr);
1504 
1505   matin->factorerrortype = mat->A->factorerrortype;
1506   PetscFunctionReturn(0);
1507 }
1508 
1509 PetscErrorCode MatPermute_MPIAIJ(Mat A,IS rowp,IS colp,Mat *B)
1510 {
1511   Mat            aA,aB,Aperm;
1512   const PetscInt *rwant,*cwant,*gcols,*ai,*bi,*aj,*bj;
1513   PetscScalar    *aa,*ba;
1514   PetscInt       i,j,m,n,ng,anz,bnz,*dnnz,*onnz,*tdnnz,*tonnz,*rdest,*cdest,*work,*gcdest;
1515   PetscSF        rowsf,sf;
1516   IS             parcolp = NULL;
1517   PetscBool      done;
1518   PetscErrorCode ierr;
1519 
1520   PetscFunctionBegin;
1521   ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
1522   ierr = ISGetIndices(rowp,&rwant);CHKERRQ(ierr);
1523   ierr = ISGetIndices(colp,&cwant);CHKERRQ(ierr);
1524   ierr = PetscMalloc3(PetscMax(m,n),&work,m,&rdest,n,&cdest);CHKERRQ(ierr);
1525 
1526   /* Invert row permutation to find out where my rows should go */
1527   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&rowsf);CHKERRQ(ierr);
1528   ierr = PetscSFSetGraphLayout(rowsf,A->rmap,A->rmap->n,NULL,PETSC_OWN_POINTER,rwant);CHKERRQ(ierr);
1529   ierr = PetscSFSetFromOptions(rowsf);CHKERRQ(ierr);
1530   for (i=0; i<m; i++) work[i] = A->rmap->rstart + i;
1531   ierr = PetscSFReduceBegin(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1532   ierr = PetscSFReduceEnd(rowsf,MPIU_INT,work,rdest,MPIU_REPLACE);CHKERRQ(ierr);
1533 
1534   /* Invert column permutation to find out where my columns should go */
1535   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1536   ierr = PetscSFSetGraphLayout(sf,A->cmap,A->cmap->n,NULL,PETSC_OWN_POINTER,cwant);CHKERRQ(ierr);
1537   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1538   for (i=0; i<n; i++) work[i] = A->cmap->rstart + i;
1539   ierr = PetscSFReduceBegin(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1540   ierr = PetscSFReduceEnd(sf,MPIU_INT,work,cdest,MPIU_REPLACE);CHKERRQ(ierr);
1541   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1542 
1543   ierr = ISRestoreIndices(rowp,&rwant);CHKERRQ(ierr);
1544   ierr = ISRestoreIndices(colp,&cwant);CHKERRQ(ierr);
1545   ierr = MatMPIAIJGetSeqAIJ(A,&aA,&aB,&gcols);CHKERRQ(ierr);
1546 
1547   /* Find out where my gcols should go */
1548   ierr = MatGetSize(aB,NULL,&ng);CHKERRQ(ierr);
1549   ierr = PetscMalloc1(ng,&gcdest);CHKERRQ(ierr);
1550   ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1551   ierr = PetscSFSetGraphLayout(sf,A->cmap,ng,NULL,PETSC_OWN_POINTER,gcols);CHKERRQ(ierr);
1552   ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1553   ierr = PetscSFBcastBegin(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1554   ierr = PetscSFBcastEnd(sf,MPIU_INT,cdest,gcdest);CHKERRQ(ierr);
1555   ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1556 
1557   ierr = PetscCalloc4(m,&dnnz,m,&onnz,m,&tdnnz,m,&tonnz);CHKERRQ(ierr);
1558   ierr = MatGetRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1559   ierr = MatGetRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1560   for (i=0; i<m; i++) {
1561     PetscInt row = rdest[i],rowner;
1562     ierr = PetscLayoutFindOwner(A->rmap,row,&rowner);CHKERRQ(ierr);
1563     for (j=ai[i]; j<ai[i+1]; j++) {
1564       PetscInt cowner,col = cdest[aj[j]];
1565       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr); /* Could build an index for the columns to eliminate this search */
1566       if (rowner == cowner) dnnz[i]++;
1567       else onnz[i]++;
1568     }
1569     for (j=bi[i]; j<bi[i+1]; j++) {
1570       PetscInt cowner,col = gcdest[bj[j]];
1571       ierr = PetscLayoutFindOwner(A->cmap,col,&cowner);CHKERRQ(ierr);
1572       if (rowner == cowner) dnnz[i]++;
1573       else onnz[i]++;
1574     }
1575   }
1576   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1577   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,dnnz,tdnnz);CHKERRQ(ierr);
1578   ierr = PetscSFBcastBegin(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1579   ierr = PetscSFBcastEnd(rowsf,MPIU_INT,onnz,tonnz);CHKERRQ(ierr);
1580   ierr = PetscSFDestroy(&rowsf);CHKERRQ(ierr);
1581 
1582   ierr = MatCreateAIJ(PetscObjectComm((PetscObject)A),A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N,0,tdnnz,0,tonnz,&Aperm);CHKERRQ(ierr);
1583   ierr = MatSeqAIJGetArray(aA,&aa);CHKERRQ(ierr);
1584   ierr = MatSeqAIJGetArray(aB,&ba);CHKERRQ(ierr);
1585   for (i=0; i<m; i++) {
1586     PetscInt *acols = dnnz,*bcols = onnz; /* Repurpose now-unneeded arrays */
1587     PetscInt j0,rowlen;
1588     rowlen = ai[i+1] - ai[i];
1589     for (j0=j=0; j<rowlen; j0=j) { /* rowlen could be larger than number of rows m, so sum in batches */
1590       for ( ; j<PetscMin(rowlen,j0+m); j++) acols[j-j0] = cdest[aj[ai[i]+j]];
1591       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,acols,aa+ai[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1592     }
1593     rowlen = bi[i+1] - bi[i];
1594     for (j0=j=0; j<rowlen; j0=j) {
1595       for ( ; j<PetscMin(rowlen,j0+m); j++) bcols[j-j0] = gcdest[bj[bi[i]+j]];
1596       ierr = MatSetValues(Aperm,1,&rdest[i],j-j0,bcols,ba+bi[i]+j0,INSERT_VALUES);CHKERRQ(ierr);
1597     }
1598   }
1599   ierr = MatAssemblyBegin(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1600   ierr = MatAssemblyEnd(Aperm,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1601   ierr = MatRestoreRowIJ(aA,0,PETSC_FALSE,PETSC_FALSE,&anz,&ai,&aj,&done);CHKERRQ(ierr);
1602   ierr = MatRestoreRowIJ(aB,0,PETSC_FALSE,PETSC_FALSE,&bnz,&bi,&bj,&done);CHKERRQ(ierr);
1603   ierr = MatSeqAIJRestoreArray(aA,&aa);CHKERRQ(ierr);
1604   ierr = MatSeqAIJRestoreArray(aB,&ba);CHKERRQ(ierr);
1605   ierr = PetscFree4(dnnz,onnz,tdnnz,tonnz);CHKERRQ(ierr);
1606   ierr = PetscFree3(work,rdest,cdest);CHKERRQ(ierr);
1607   ierr = PetscFree(gcdest);CHKERRQ(ierr);
1608   if (parcolp) {ierr = ISDestroy(&colp);CHKERRQ(ierr);}
1609   *B = Aperm;
1610   PetscFunctionReturn(0);
1611 }
1612 
1613 PetscErrorCode  MatGetGhosts_MPIAIJ(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
1614 {
1615   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1616   PetscErrorCode ierr;
1617 
1618   PetscFunctionBegin;
1619   ierr = MatGetSize(aij->B,NULL,nghosts);CHKERRQ(ierr);
1620   if (ghosts) *ghosts = aij->garray;
1621   PetscFunctionReturn(0);
1622 }
1623 
1624 PetscErrorCode MatGetInfo_MPIAIJ(Mat matin,MatInfoType flag,MatInfo *info)
1625 {
1626   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1627   Mat            A    = mat->A,B = mat->B;
1628   PetscErrorCode ierr;
1629   PetscReal      isend[5],irecv[5];
1630 
1631   PetscFunctionBegin;
1632   info->block_size = 1.0;
1633   ierr             = MatGetInfo(A,MAT_LOCAL,info);CHKERRQ(ierr);
1634 
1635   isend[0] = info->nz_used; isend[1] = info->nz_allocated; isend[2] = info->nz_unneeded;
1636   isend[3] = info->memory;  isend[4] = info->mallocs;
1637 
1638   ierr = MatGetInfo(B,MAT_LOCAL,info);CHKERRQ(ierr);
1639 
1640   isend[0] += info->nz_used; isend[1] += info->nz_allocated; isend[2] += info->nz_unneeded;
1641   isend[3] += info->memory;  isend[4] += info->mallocs;
1642   if (flag == MAT_LOCAL) {
1643     info->nz_used      = isend[0];
1644     info->nz_allocated = isend[1];
1645     info->nz_unneeded  = isend[2];
1646     info->memory       = isend[3];
1647     info->mallocs      = isend[4];
1648   } else if (flag == MAT_GLOBAL_MAX) {
1649     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1650 
1651     info->nz_used      = irecv[0];
1652     info->nz_allocated = irecv[1];
1653     info->nz_unneeded  = irecv[2];
1654     info->memory       = irecv[3];
1655     info->mallocs      = irecv[4];
1656   } else if (flag == MAT_GLOBAL_SUM) {
1657     ierr = MPIU_Allreduce(isend,irecv,5,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)matin));CHKERRQ(ierr);
1658 
1659     info->nz_used      = irecv[0];
1660     info->nz_allocated = irecv[1];
1661     info->nz_unneeded  = irecv[2];
1662     info->memory       = irecv[3];
1663     info->mallocs      = irecv[4];
1664   }
1665   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1666   info->fill_ratio_needed = 0;
1667   info->factor_mallocs    = 0;
1668   PetscFunctionReturn(0);
1669 }
1670 
1671 PetscErrorCode MatSetOption_MPIAIJ(Mat A,MatOption op,PetscBool flg)
1672 {
1673   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
1674   PetscErrorCode ierr;
1675 
1676   PetscFunctionBegin;
1677   switch (op) {
1678   case MAT_NEW_NONZERO_LOCATIONS:
1679   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1680   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1681   case MAT_KEEP_NONZERO_PATTERN:
1682   case MAT_NEW_NONZERO_LOCATION_ERR:
1683   case MAT_USE_INODES:
1684   case MAT_IGNORE_ZERO_ENTRIES:
1685     MatCheckPreallocated(A,1);
1686     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1687     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1688     break;
1689   case MAT_ROW_ORIENTED:
1690     MatCheckPreallocated(A,1);
1691     a->roworiented = flg;
1692 
1693     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1694     ierr = MatSetOption(a->B,op,flg);CHKERRQ(ierr);
1695     break;
1696   case MAT_NEW_DIAGONALS:
1697     ierr = PetscInfo1(A,"Option %s ignored\n",MatOptions[op]);CHKERRQ(ierr);
1698     break;
1699   case MAT_IGNORE_OFF_PROC_ENTRIES:
1700     a->donotstash = flg;
1701     break;
1702   case MAT_SPD:
1703     A->spd_set = PETSC_TRUE;
1704     A->spd     = flg;
1705     if (flg) {
1706       A->symmetric                  = PETSC_TRUE;
1707       A->structurally_symmetric     = PETSC_TRUE;
1708       A->symmetric_set              = PETSC_TRUE;
1709       A->structurally_symmetric_set = PETSC_TRUE;
1710     }
1711     break;
1712   case MAT_SYMMETRIC:
1713     MatCheckPreallocated(A,1);
1714     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1715     break;
1716   case MAT_STRUCTURALLY_SYMMETRIC:
1717     MatCheckPreallocated(A,1);
1718     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1719     break;
1720   case MAT_HERMITIAN:
1721     MatCheckPreallocated(A,1);
1722     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1723     break;
1724   case MAT_SYMMETRY_ETERNAL:
1725     MatCheckPreallocated(A,1);
1726     ierr = MatSetOption(a->A,op,flg);CHKERRQ(ierr);
1727     break;
1728   case MAT_SUBMAT_SINGLEIS:
1729     A->submat_singleis = flg;
1730     break;
1731   default:
1732     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"unknown option %d",op);
1733   }
1734   PetscFunctionReturn(0);
1735 }
1736 
1737 PetscErrorCode MatGetRow_MPIAIJ(Mat matin,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1738 {
1739   Mat_MPIAIJ     *mat = (Mat_MPIAIJ*)matin->data;
1740   PetscScalar    *vworkA,*vworkB,**pvA,**pvB,*v_p;
1741   PetscErrorCode ierr;
1742   PetscInt       i,*cworkA,*cworkB,**pcA,**pcB,cstart = matin->cmap->rstart;
1743   PetscInt       nztot,nzA,nzB,lrow,rstart = matin->rmap->rstart,rend = matin->rmap->rend;
1744   PetscInt       *cmap,*idx_p;
1745 
1746   PetscFunctionBegin;
1747   if (mat->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Already active");
1748   mat->getrowactive = PETSC_TRUE;
1749 
1750   if (!mat->rowvalues && (idx || v)) {
1751     /*
1752         allocate enough space to hold information from the longest row.
1753     */
1754     Mat_SeqAIJ *Aa = (Mat_SeqAIJ*)mat->A->data,*Ba = (Mat_SeqAIJ*)mat->B->data;
1755     PetscInt   max = 1,tmp;
1756     for (i=0; i<matin->rmap->n; i++) {
1757       tmp = Aa->i[i+1] - Aa->i[i] + Ba->i[i+1] - Ba->i[i];
1758       if (max < tmp) max = tmp;
1759     }
1760     ierr = PetscMalloc2(max,&mat->rowvalues,max,&mat->rowindices);CHKERRQ(ierr);
1761   }
1762 
1763   if (row < rstart || row >= rend) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Only local rows");
1764   lrow = row - rstart;
1765 
1766   pvA = &vworkA; pcA = &cworkA; pvB = &vworkB; pcB = &cworkB;
1767   if (!v)   {pvA = 0; pvB = 0;}
1768   if (!idx) {pcA = 0; if (!v) pcB = 0;}
1769   ierr  = (*mat->A->ops->getrow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1770   ierr  = (*mat->B->ops->getrow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1771   nztot = nzA + nzB;
1772 
1773   cmap = mat->garray;
1774   if (v  || idx) {
1775     if (nztot) {
1776       /* Sort by increasing column numbers, assuming A and B already sorted */
1777       PetscInt imark = -1;
1778       if (v) {
1779         *v = v_p = mat->rowvalues;
1780         for (i=0; i<nzB; i++) {
1781           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1782           else break;
1783         }
1784         imark = i;
1785         for (i=0; i<nzA; i++)     v_p[imark+i] = vworkA[i];
1786         for (i=imark; i<nzB; i++) v_p[nzA+i]   = vworkB[i];
1787       }
1788       if (idx) {
1789         *idx = idx_p = mat->rowindices;
1790         if (imark > -1) {
1791           for (i=0; i<imark; i++) {
1792             idx_p[i] = cmap[cworkB[i]];
1793           }
1794         } else {
1795           for (i=0; i<nzB; i++) {
1796             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1797             else break;
1798           }
1799           imark = i;
1800         }
1801         for (i=0; i<nzA; i++)     idx_p[imark+i] = cstart + cworkA[i];
1802         for (i=imark; i<nzB; i++) idx_p[nzA+i]   = cmap[cworkB[i]];
1803       }
1804     } else {
1805       if (idx) *idx = 0;
1806       if (v)   *v   = 0;
1807     }
1808   }
1809   *nz  = nztot;
1810   ierr = (*mat->A->ops->restorerow)(mat->A,lrow,&nzA,pcA,pvA);CHKERRQ(ierr);
1811   ierr = (*mat->B->ops->restorerow)(mat->B,lrow,&nzB,pcB,pvB);CHKERRQ(ierr);
1812   PetscFunctionReturn(0);
1813 }
1814 
1815 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
1816 {
1817   Mat_MPIAIJ *aij = (Mat_MPIAIJ*)mat->data;
1818 
1819   PetscFunctionBegin;
1820   if (!aij->getrowactive) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"MatGetRow() must be called first");
1821   aij->getrowactive = PETSC_FALSE;
1822   PetscFunctionReturn(0);
1823 }
1824 
1825 PetscErrorCode MatNorm_MPIAIJ(Mat mat,NormType type,PetscReal *norm)
1826 {
1827   Mat_MPIAIJ     *aij  = (Mat_MPIAIJ*)mat->data;
1828   Mat_SeqAIJ     *amat = (Mat_SeqAIJ*)aij->A->data,*bmat = (Mat_SeqAIJ*)aij->B->data;
1829   PetscErrorCode ierr;
1830   PetscInt       i,j,cstart = mat->cmap->rstart;
1831   PetscReal      sum = 0.0;
1832   MatScalar      *v;
1833 
1834   PetscFunctionBegin;
1835   if (aij->size == 1) {
1836     ierr =  MatNorm(aij->A,type,norm);CHKERRQ(ierr);
1837   } else {
1838     if (type == NORM_FROBENIUS) {
1839       v = amat->a;
1840       for (i=0; i<amat->nz; i++) {
1841         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1842       }
1843       v = bmat->a;
1844       for (i=0; i<bmat->nz; i++) {
1845         sum += PetscRealPart(PetscConj(*v)*(*v)); v++;
1846       }
1847       ierr  = MPIU_Allreduce(&sum,norm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1848       *norm = PetscSqrtReal(*norm);
1849       ierr = PetscLogFlops(2*amat->nz+2*bmat->nz);CHKERRQ(ierr);
1850     } else if (type == NORM_1) { /* max column norm */
1851       PetscReal *tmp,*tmp2;
1852       PetscInt  *jj,*garray = aij->garray;
1853       ierr  = PetscCalloc1(mat->cmap->N+1,&tmp);CHKERRQ(ierr);
1854       ierr  = PetscMalloc1(mat->cmap->N+1,&tmp2);CHKERRQ(ierr);
1855       *norm = 0.0;
1856       v     = amat->a; jj = amat->j;
1857       for (j=0; j<amat->nz; j++) {
1858         tmp[cstart + *jj++] += PetscAbsScalar(*v);  v++;
1859       }
1860       v = bmat->a; jj = bmat->j;
1861       for (j=0; j<bmat->nz; j++) {
1862         tmp[garray[*jj++]] += PetscAbsScalar(*v); v++;
1863       }
1864       ierr = MPIU_Allreduce(tmp,tmp2,mat->cmap->N,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1865       for (j=0; j<mat->cmap->N; j++) {
1866         if (tmp2[j] > *norm) *norm = tmp2[j];
1867       }
1868       ierr = PetscFree(tmp);CHKERRQ(ierr);
1869       ierr = PetscFree(tmp2);CHKERRQ(ierr);
1870       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1871     } else if (type == NORM_INFINITY) { /* max row norm */
1872       PetscReal ntemp = 0.0;
1873       for (j=0; j<aij->A->rmap->n; j++) {
1874         v   = amat->a + amat->i[j];
1875         sum = 0.0;
1876         for (i=0; i<amat->i[j+1]-amat->i[j]; i++) {
1877           sum += PetscAbsScalar(*v); v++;
1878         }
1879         v = bmat->a + bmat->i[j];
1880         for (i=0; i<bmat->i[j+1]-bmat->i[j]; i++) {
1881           sum += PetscAbsScalar(*v); v++;
1882         }
1883         if (sum > ntemp) ntemp = sum;
1884       }
1885       ierr = MPIU_Allreduce(&ntemp,norm,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
1886       ierr = PetscLogFlops(PetscMax(amat->nz+bmat->nz-1,0));CHKERRQ(ierr);
1887     } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No support for two norm");
1888   }
1889   PetscFunctionReturn(0);
1890 }
1891 
1892 PetscErrorCode MatTranspose_MPIAIJ(Mat A,MatReuse reuse,Mat *matout)
1893 {
1894   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data;
1895   Mat_SeqAIJ     *Aloc=(Mat_SeqAIJ*)a->A->data,*Bloc=(Mat_SeqAIJ*)a->B->data;
1896   PetscErrorCode ierr;
1897   PetscInt       M      = A->rmap->N,N = A->cmap->N,ma,na,mb,nb,*ai,*aj,*bi,*bj,row,*cols,*cols_tmp,i;
1898   PetscInt       cstart = A->cmap->rstart,ncol;
1899   Mat            B;
1900   MatScalar      *array;
1901 
1902   PetscFunctionBegin;
1903   if (reuse == MAT_INPLACE_MATRIX && M != N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Square matrix only for in-place");
1904 
1905   ma = A->rmap->n; na = A->cmap->n; mb = a->B->rmap->n; nb = a->B->cmap->n;
1906   ai = Aloc->i; aj = Aloc->j;
1907   bi = Bloc->i; bj = Bloc->j;
1908   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1909     PetscInt             *d_nnz,*g_nnz,*o_nnz;
1910     PetscSFNode          *oloc;
1911     PETSC_UNUSED PetscSF sf;
1912 
1913     ierr = PetscMalloc4(na,&d_nnz,na,&o_nnz,nb,&g_nnz,nb,&oloc);CHKERRQ(ierr);
1914     /* compute d_nnz for preallocation */
1915     ierr = PetscMemzero(d_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1916     for (i=0; i<ai[ma]; i++) {
1917       d_nnz[aj[i]]++;
1918       aj[i] += cstart; /* global col index to be used by MatSetValues() */
1919     }
1920     /* compute local off-diagonal contributions */
1921     ierr = PetscMemzero(g_nnz,nb*sizeof(PetscInt));CHKERRQ(ierr);
1922     for (i=0; i<bi[ma]; i++) g_nnz[bj[i]]++;
1923     /* map those to global */
1924     ierr = PetscSFCreate(PetscObjectComm((PetscObject)A),&sf);CHKERRQ(ierr);
1925     ierr = PetscSFSetGraphLayout(sf,A->cmap,nb,NULL,PETSC_USE_POINTER,a->garray);CHKERRQ(ierr);
1926     ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
1927     ierr = PetscMemzero(o_nnz,na*sizeof(PetscInt));CHKERRQ(ierr);
1928     ierr = PetscSFReduceBegin(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1929     ierr = PetscSFReduceEnd(sf,MPIU_INT,g_nnz,o_nnz,MPIU_SUM);CHKERRQ(ierr);
1930     ierr = PetscSFDestroy(&sf);CHKERRQ(ierr);
1931 
1932     ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
1933     ierr = MatSetSizes(B,A->cmap->n,A->rmap->n,N,M);CHKERRQ(ierr);
1934     ierr = MatSetBlockSizes(B,PetscAbs(A->cmap->bs),PetscAbs(A->rmap->bs));CHKERRQ(ierr);
1935     ierr = MatSetType(B,((PetscObject)A)->type_name);CHKERRQ(ierr);
1936     ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
1937     ierr = PetscFree4(d_nnz,o_nnz,g_nnz,oloc);CHKERRQ(ierr);
1938   } else {
1939     B    = *matout;
1940     ierr = MatSetOption(B,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
1941     for (i=0; i<ai[ma]; i++) aj[i] += cstart; /* global col index to be used by MatSetValues() */
1942   }
1943 
1944   /* copy over the A part */
1945   array = Aloc->a;
1946   row   = A->rmap->rstart;
1947   for (i=0; i<ma; i++) {
1948     ncol = ai[i+1]-ai[i];
1949     ierr = MatSetValues(B,ncol,aj,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1950     row++;
1951     array += ncol; aj += ncol;
1952   }
1953   aj = Aloc->j;
1954   for (i=0; i<ai[ma]; i++) aj[i] -= cstart; /* resume local col index */
1955 
1956   /* copy over the B part */
1957   ierr  = PetscCalloc1(bi[mb],&cols);CHKERRQ(ierr);
1958   array = Bloc->a;
1959   row   = A->rmap->rstart;
1960   for (i=0; i<bi[mb]; i++) cols[i] = a->garray[bj[i]];
1961   cols_tmp = cols;
1962   for (i=0; i<mb; i++) {
1963     ncol = bi[i+1]-bi[i];
1964     ierr = MatSetValues(B,ncol,cols_tmp,1,&row,array,INSERT_VALUES);CHKERRQ(ierr);
1965     row++;
1966     array += ncol; cols_tmp += ncol;
1967   }
1968   ierr = PetscFree(cols);CHKERRQ(ierr);
1969 
1970   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1971   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1972   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1973     *matout = B;
1974   } else {
1975     ierr = MatHeaderMerge(A,&B);CHKERRQ(ierr);
1976   }
1977   PetscFunctionReturn(0);
1978 }
1979 
1980 PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat,Vec ll,Vec rr)
1981 {
1982   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
1983   Mat            a    = aij->A,b = aij->B;
1984   PetscErrorCode ierr;
1985   PetscInt       s1,s2,s3;
1986 
1987   PetscFunctionBegin;
1988   ierr = MatGetLocalSize(mat,&s2,&s3);CHKERRQ(ierr);
1989   if (rr) {
1990     ierr = VecGetLocalSize(rr,&s1);CHKERRQ(ierr);
1991     if (s1!=s3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"right vector non-conforming local size");
1992     /* Overlap communication with computation. */
1993     ierr = VecScatterBegin(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
1994   }
1995   if (ll) {
1996     ierr = VecGetLocalSize(ll,&s1);CHKERRQ(ierr);
1997     if (s1!=s2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"left vector non-conforming local size");
1998     ierr = (*b->ops->diagonalscale)(b,ll,0);CHKERRQ(ierr);
1999   }
2000   /* scale  the diagonal block */
2001   ierr = (*a->ops->diagonalscale)(a,ll,rr);CHKERRQ(ierr);
2002 
2003   if (rr) {
2004     /* Do a scatter end and then right scale the off-diagonal block */
2005     ierr = VecScatterEnd(aij->Mvctx,rr,aij->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
2006     ierr = (*b->ops->diagonalscale)(b,0,aij->lvec);CHKERRQ(ierr);
2007   }
2008   PetscFunctionReturn(0);
2009 }
2010 
2011 PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2012 {
2013   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2014   PetscErrorCode ierr;
2015 
2016   PetscFunctionBegin;
2017   ierr = MatSetUnfactored(a->A);CHKERRQ(ierr);
2018   PetscFunctionReturn(0);
2019 }
2020 
2021 PetscErrorCode MatEqual_MPIAIJ(Mat A,Mat B,PetscBool  *flag)
2022 {
2023   Mat_MPIAIJ     *matB = (Mat_MPIAIJ*)B->data,*matA = (Mat_MPIAIJ*)A->data;
2024   Mat            a,b,c,d;
2025   PetscBool      flg;
2026   PetscErrorCode ierr;
2027 
2028   PetscFunctionBegin;
2029   a = matA->A; b = matA->B;
2030   c = matB->A; d = matB->B;
2031 
2032   ierr = MatEqual(a,c,&flg);CHKERRQ(ierr);
2033   if (flg) {
2034     ierr = MatEqual(b,d,&flg);CHKERRQ(ierr);
2035   }
2036   ierr = MPIU_Allreduce(&flg,flag,1,MPIU_BOOL,MPI_LAND,PetscObjectComm((PetscObject)A));CHKERRQ(ierr);
2037   PetscFunctionReturn(0);
2038 }
2039 
2040 PetscErrorCode MatCopy_MPIAIJ(Mat A,Mat B,MatStructure str)
2041 {
2042   PetscErrorCode ierr;
2043   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2044   Mat_MPIAIJ     *b = (Mat_MPIAIJ*)B->data;
2045 
2046   PetscFunctionBegin;
2047   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2048   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2049     /* because of the column compression in the off-processor part of the matrix a->B,
2050        the number of columns in a->B and b->B may be different, hence we cannot call
2051        the MatCopy() directly on the two parts. If need be, we can provide a more
2052        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2053        then copying the submatrices */
2054     ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
2055   } else {
2056     ierr = MatCopy(a->A,b->A,str);CHKERRQ(ierr);
2057     ierr = MatCopy(a->B,b->B,str);CHKERRQ(ierr);
2058   }
2059   PetscFunctionReturn(0);
2060 }
2061 
2062 PetscErrorCode MatSetUp_MPIAIJ(Mat A)
2063 {
2064   PetscErrorCode ierr;
2065 
2066   PetscFunctionBegin;
2067   ierr =  MatMPIAIJSetPreallocation(A,PETSC_DEFAULT,0,PETSC_DEFAULT,0);CHKERRQ(ierr);
2068   PetscFunctionReturn(0);
2069 }
2070 
2071 /*
2072    Computes the number of nonzeros per row needed for preallocation when X and Y
2073    have different nonzero structure.
2074 */
2075 PetscErrorCode MatAXPYGetPreallocation_MPIX_private(PetscInt m,const PetscInt *xi,const PetscInt *xj,const PetscInt *xltog,const PetscInt *yi,const PetscInt *yj,const PetscInt *yltog,PetscInt *nnz)
2076 {
2077   PetscInt       i,j,k,nzx,nzy;
2078 
2079   PetscFunctionBegin;
2080   /* Set the number of nonzeros in the new matrix */
2081   for (i=0; i<m; i++) {
2082     const PetscInt *xjj = xj+xi[i],*yjj = yj+yi[i];
2083     nzx = xi[i+1] - xi[i];
2084     nzy = yi[i+1] - yi[i];
2085     nnz[i] = 0;
2086     for (j=0,k=0; j<nzx; j++) {                   /* Point in X */
2087       for (; k<nzy && yltog[yjj[k]]<xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2088       if (k<nzy && yltog[yjj[k]]==xltog[xjj[j]]) k++;             /* Skip duplicate */
2089       nnz[i]++;
2090     }
2091     for (; k<nzy; k++) nnz[i]++;
2092   }
2093   PetscFunctionReturn(0);
2094 }
2095 
2096 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2097 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y,const PetscInt *yltog,Mat X,const PetscInt *xltog,PetscInt *nnz)
2098 {
2099   PetscErrorCode ierr;
2100   PetscInt       m = Y->rmap->N;
2101   Mat_SeqAIJ     *x = (Mat_SeqAIJ*)X->data;
2102   Mat_SeqAIJ     *y = (Mat_SeqAIJ*)Y->data;
2103 
2104   PetscFunctionBegin;
2105   ierr = MatAXPYGetPreallocation_MPIX_private(m,x->i,x->j,xltog,y->i,y->j,yltog,nnz);CHKERRQ(ierr);
2106   PetscFunctionReturn(0);
2107 }
2108 
2109 PetscErrorCode MatAXPY_MPIAIJ(Mat Y,PetscScalar a,Mat X,MatStructure str)
2110 {
2111   PetscErrorCode ierr;
2112   Mat_MPIAIJ     *xx = (Mat_MPIAIJ*)X->data,*yy = (Mat_MPIAIJ*)Y->data;
2113   PetscBLASInt   bnz,one=1;
2114   Mat_SeqAIJ     *x,*y;
2115 
2116   PetscFunctionBegin;
2117   if (str == SAME_NONZERO_PATTERN) {
2118     PetscScalar alpha = a;
2119     x    = (Mat_SeqAIJ*)xx->A->data;
2120     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2121     y    = (Mat_SeqAIJ*)yy->A->data;
2122     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2123     x    = (Mat_SeqAIJ*)xx->B->data;
2124     y    = (Mat_SeqAIJ*)yy->B->data;
2125     ierr = PetscBLASIntCast(x->nz,&bnz);CHKERRQ(ierr);
2126     PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&bnz,&alpha,x->a,&one,y->a,&one));
2127     ierr = PetscObjectStateIncrease((PetscObject)Y);CHKERRQ(ierr);
2128   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2129     ierr = MatAXPY_Basic(Y,a,X,str);CHKERRQ(ierr);
2130   } else {
2131     Mat      B;
2132     PetscInt *nnz_d,*nnz_o;
2133     ierr = PetscMalloc1(yy->A->rmap->N,&nnz_d);CHKERRQ(ierr);
2134     ierr = PetscMalloc1(yy->B->rmap->N,&nnz_o);CHKERRQ(ierr);
2135     ierr = MatCreate(PetscObjectComm((PetscObject)Y),&B);CHKERRQ(ierr);
2136     ierr = PetscObjectSetName((PetscObject)B,((PetscObject)Y)->name);CHKERRQ(ierr);
2137     ierr = MatSetSizes(B,Y->rmap->n,Y->cmap->n,Y->rmap->N,Y->cmap->N);CHKERRQ(ierr);
2138     ierr = MatSetBlockSizesFromMats(B,Y,Y);CHKERRQ(ierr);
2139     ierr = MatSetType(B,MATMPIAIJ);CHKERRQ(ierr);
2140     ierr = MatAXPYGetPreallocation_SeqAIJ(yy->A,xx->A,nnz_d);CHKERRQ(ierr);
2141     ierr = MatAXPYGetPreallocation_MPIAIJ(yy->B,yy->garray,xx->B,xx->garray,nnz_o);CHKERRQ(ierr);
2142     ierr = MatMPIAIJSetPreallocation(B,0,nnz_d,0,nnz_o);CHKERRQ(ierr);
2143     ierr = MatAXPY_BasicWithPreallocation(B,Y,a,X,str);CHKERRQ(ierr);
2144     ierr = MatHeaderReplace(Y,&B);CHKERRQ(ierr);
2145     ierr = PetscFree(nnz_d);CHKERRQ(ierr);
2146     ierr = PetscFree(nnz_o);CHKERRQ(ierr);
2147   }
2148   PetscFunctionReturn(0);
2149 }
2150 
2151 extern PetscErrorCode  MatConjugate_SeqAIJ(Mat);
2152 
2153 PetscErrorCode  MatConjugate_MPIAIJ(Mat mat)
2154 {
2155 #if defined(PETSC_USE_COMPLEX)
2156   PetscErrorCode ierr;
2157   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2158 
2159   PetscFunctionBegin;
2160   ierr = MatConjugate_SeqAIJ(aij->A);CHKERRQ(ierr);
2161   ierr = MatConjugate_SeqAIJ(aij->B);CHKERRQ(ierr);
2162 #else
2163   PetscFunctionBegin;
2164 #endif
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2169 {
2170   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2171   PetscErrorCode ierr;
2172 
2173   PetscFunctionBegin;
2174   ierr = MatRealPart(a->A);CHKERRQ(ierr);
2175   ierr = MatRealPart(a->B);CHKERRQ(ierr);
2176   PetscFunctionReturn(0);
2177 }
2178 
2179 PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2180 {
2181   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2182   PetscErrorCode ierr;
2183 
2184   PetscFunctionBegin;
2185   ierr = MatImaginaryPart(a->A);CHKERRQ(ierr);
2186   ierr = MatImaginaryPart(a->B);CHKERRQ(ierr);
2187   PetscFunctionReturn(0);
2188 }
2189 
2190 PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2191 {
2192   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2193   PetscErrorCode ierr;
2194   PetscInt       i,*idxb = 0;
2195   PetscScalar    *va,*vb;
2196   Vec            vtmp;
2197 
2198   PetscFunctionBegin;
2199   ierr = MatGetRowMaxAbs(a->A,v,idx);CHKERRQ(ierr);
2200   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2201   if (idx) {
2202     for (i=0; i<A->rmap->n; i++) {
2203       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2204     }
2205   }
2206 
2207   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2208   if (idx) {
2209     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2210   }
2211   ierr = MatGetRowMaxAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2212   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2213 
2214   for (i=0; i<A->rmap->n; i++) {
2215     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2216       va[i] = vb[i];
2217       if (idx) idx[i] = a->garray[idxb[i]];
2218     }
2219   }
2220 
2221   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2222   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2223   ierr = PetscFree(idxb);CHKERRQ(ierr);
2224   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2225   PetscFunctionReturn(0);
2226 }
2227 
2228 PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2229 {
2230   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2231   PetscErrorCode ierr;
2232   PetscInt       i,*idxb = 0;
2233   PetscScalar    *va,*vb;
2234   Vec            vtmp;
2235 
2236   PetscFunctionBegin;
2237   ierr = MatGetRowMinAbs(a->A,v,idx);CHKERRQ(ierr);
2238   ierr = VecGetArray(v,&va);CHKERRQ(ierr);
2239   if (idx) {
2240     for (i=0; i<A->cmap->n; i++) {
2241       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2242     }
2243   }
2244 
2245   ierr = VecCreateSeq(PETSC_COMM_SELF,A->rmap->n,&vtmp);CHKERRQ(ierr);
2246   if (idx) {
2247     ierr = PetscMalloc1(A->rmap->n,&idxb);CHKERRQ(ierr);
2248   }
2249   ierr = MatGetRowMinAbs(a->B,vtmp,idxb);CHKERRQ(ierr);
2250   ierr = VecGetArray(vtmp,&vb);CHKERRQ(ierr);
2251 
2252   for (i=0; i<A->rmap->n; i++) {
2253     if (PetscAbsScalar(va[i]) > PetscAbsScalar(vb[i])) {
2254       va[i] = vb[i];
2255       if (idx) idx[i] = a->garray[idxb[i]];
2256     }
2257   }
2258 
2259   ierr = VecRestoreArray(v,&va);CHKERRQ(ierr);
2260   ierr = VecRestoreArray(vtmp,&vb);CHKERRQ(ierr);
2261   ierr = PetscFree(idxb);CHKERRQ(ierr);
2262   ierr = VecDestroy(&vtmp);CHKERRQ(ierr);
2263   PetscFunctionReturn(0);
2264 }
2265 
2266 PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2267 {
2268   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2269   PetscInt       n      = A->rmap->n;
2270   PetscInt       cstart = A->cmap->rstart;
2271   PetscInt       *cmap  = mat->garray;
2272   PetscInt       *diagIdx, *offdiagIdx;
2273   Vec            diagV, offdiagV;
2274   PetscScalar    *a, *diagA, *offdiagA;
2275   PetscInt       r;
2276   PetscErrorCode ierr;
2277 
2278   PetscFunctionBegin;
2279   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2280   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &diagV);CHKERRQ(ierr);
2281   ierr = VecCreateSeq(PetscObjectComm((PetscObject)A), n, &offdiagV);CHKERRQ(ierr);
2282   ierr = MatGetRowMin(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2283   ierr = MatGetRowMin(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2284   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2285   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2286   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2287   for (r = 0; r < n; ++r) {
2288     if (PetscAbsScalar(diagA[r]) <= PetscAbsScalar(offdiagA[r])) {
2289       a[r]   = diagA[r];
2290       idx[r] = cstart + diagIdx[r];
2291     } else {
2292       a[r]   = offdiagA[r];
2293       idx[r] = cmap[offdiagIdx[r]];
2294     }
2295   }
2296   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2297   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2298   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2299   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2300   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2301   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2302   PetscFunctionReturn(0);
2303 }
2304 
2305 PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2306 {
2307   Mat_MPIAIJ     *mat   = (Mat_MPIAIJ*) A->data;
2308   PetscInt       n      = A->rmap->n;
2309   PetscInt       cstart = A->cmap->rstart;
2310   PetscInt       *cmap  = mat->garray;
2311   PetscInt       *diagIdx, *offdiagIdx;
2312   Vec            diagV, offdiagV;
2313   PetscScalar    *a, *diagA, *offdiagA;
2314   PetscInt       r;
2315   PetscErrorCode ierr;
2316 
2317   PetscFunctionBegin;
2318   ierr = PetscMalloc2(n,&diagIdx,n,&offdiagIdx);CHKERRQ(ierr);
2319   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &diagV);CHKERRQ(ierr);
2320   ierr = VecCreateSeq(PETSC_COMM_SELF, n, &offdiagV);CHKERRQ(ierr);
2321   ierr = MatGetRowMax(mat->A, diagV,    diagIdx);CHKERRQ(ierr);
2322   ierr = MatGetRowMax(mat->B, offdiagV, offdiagIdx);CHKERRQ(ierr);
2323   ierr = VecGetArray(v,        &a);CHKERRQ(ierr);
2324   ierr = VecGetArray(diagV,    &diagA);CHKERRQ(ierr);
2325   ierr = VecGetArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2326   for (r = 0; r < n; ++r) {
2327     if (PetscAbsScalar(diagA[r]) >= PetscAbsScalar(offdiagA[r])) {
2328       a[r]   = diagA[r];
2329       idx[r] = cstart + diagIdx[r];
2330     } else {
2331       a[r]   = offdiagA[r];
2332       idx[r] = cmap[offdiagIdx[r]];
2333     }
2334   }
2335   ierr = VecRestoreArray(v,        &a);CHKERRQ(ierr);
2336   ierr = VecRestoreArray(diagV,    &diagA);CHKERRQ(ierr);
2337   ierr = VecRestoreArray(offdiagV, &offdiagA);CHKERRQ(ierr);
2338   ierr = VecDestroy(&diagV);CHKERRQ(ierr);
2339   ierr = VecDestroy(&offdiagV);CHKERRQ(ierr);
2340   ierr = PetscFree2(diagIdx, offdiagIdx);CHKERRQ(ierr);
2341   PetscFunctionReturn(0);
2342 }
2343 
2344 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat,Mat *newmat)
2345 {
2346   PetscErrorCode ierr;
2347   Mat            *dummy;
2348 
2349   PetscFunctionBegin;
2350   ierr    = MatCreateSubMatrix_MPIAIJ_All(mat,MAT_DO_NOT_GET_VALUES,MAT_INITIAL_MATRIX,&dummy);CHKERRQ(ierr);
2351   *newmat = *dummy;
2352   ierr    = PetscFree(dummy);CHKERRQ(ierr);
2353   PetscFunctionReturn(0);
2354 }
2355 
2356 PetscErrorCode  MatInvertBlockDiagonal_MPIAIJ(Mat A,const PetscScalar **values)
2357 {
2358   Mat_MPIAIJ     *a = (Mat_MPIAIJ*) A->data;
2359   PetscErrorCode ierr;
2360 
2361   PetscFunctionBegin;
2362   ierr = MatInvertBlockDiagonal(a->A,values);CHKERRQ(ierr);
2363   A->factorerrortype = a->A->factorerrortype;
2364   PetscFunctionReturn(0);
2365 }
2366 
2367 static PetscErrorCode  MatSetRandom_MPIAIJ(Mat x,PetscRandom rctx)
2368 {
2369   PetscErrorCode ierr;
2370   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)x->data;
2371 
2372   PetscFunctionBegin;
2373   ierr = MatSetRandom(aij->A,rctx);CHKERRQ(ierr);
2374   ierr = MatSetRandom(aij->B,rctx);CHKERRQ(ierr);
2375   ierr = MatAssemblyBegin(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2376   ierr = MatAssemblyEnd(x,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2377   PetscFunctionReturn(0);
2378 }
2379 
2380 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A,PetscBool sc)
2381 {
2382   PetscFunctionBegin;
2383   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2384   else A->ops->increaseoverlap    = MatIncreaseOverlap_MPIAIJ;
2385   PetscFunctionReturn(0);
2386 }
2387 
2388 /*@
2389    MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2390 
2391    Collective on Mat
2392 
2393    Input Parameters:
2394 +    A - the matrix
2395 -    sc - PETSC_TRUE indicates use the scalable algorithm (default is not to use the scalable algorithm)
2396 
2397  Level: advanced
2398 
2399 @*/
2400 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A,PetscBool sc)
2401 {
2402   PetscErrorCode       ierr;
2403 
2404   PetscFunctionBegin;
2405   ierr = PetscTryMethod(A,"MatMPIAIJSetUseScalableIncreaseOverlap_C",(Mat,PetscBool),(A,sc));CHKERRQ(ierr);
2406   PetscFunctionReturn(0);
2407 }
2408 
2409 PetscErrorCode MatSetFromOptions_MPIAIJ(PetscOptionItems *PetscOptionsObject,Mat A)
2410 {
2411   PetscErrorCode       ierr;
2412   PetscBool            sc = PETSC_FALSE,flg;
2413 
2414   PetscFunctionBegin;
2415   ierr = PetscOptionsHead(PetscOptionsObject,"MPIAIJ options");CHKERRQ(ierr);
2416   ierr = PetscObjectOptionsBegin((PetscObject)A);
2417     if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2418     ierr = PetscOptionsBool("-mat_increase_overlap_scalable","Use a scalable algorithm to compute the overlap","MatIncreaseOverlap",sc,&sc,&flg);CHKERRQ(ierr);
2419     if (flg) {
2420       ierr = MatMPIAIJSetUseScalableIncreaseOverlap(A,sc);CHKERRQ(ierr);
2421     }
2422   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2423   PetscFunctionReturn(0);
2424 }
2425 
2426 PetscErrorCode MatShift_MPIAIJ(Mat Y,PetscScalar a)
2427 {
2428   PetscErrorCode ierr;
2429   Mat_MPIAIJ     *maij = (Mat_MPIAIJ*)Y->data;
2430   Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)maij->A->data;
2431 
2432   PetscFunctionBegin;
2433   if (!Y->preallocated) {
2434     ierr = MatMPIAIJSetPreallocation(Y,1,NULL,0,NULL);CHKERRQ(ierr);
2435   } else if (!aij->nz) {
2436     PetscInt nonew = aij->nonew;
2437     ierr = MatSeqAIJSetPreallocation(maij->A,1,NULL);CHKERRQ(ierr);
2438     aij->nonew = nonew;
2439   }
2440   ierr = MatShift_Basic(Y,a);CHKERRQ(ierr);
2441   PetscFunctionReturn(0);
2442 }
2443 
2444 PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A,PetscBool  *missing,PetscInt *d)
2445 {
2446   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
2447   PetscErrorCode ierr;
2448 
2449   PetscFunctionBegin;
2450   if (A->rmap->n != A->cmap->n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only works for square matrices");
2451   ierr = MatMissingDiagonal(a->A,missing,d);CHKERRQ(ierr);
2452   if (d) {
2453     PetscInt rstart;
2454     ierr = MatGetOwnershipRange(A,&rstart,NULL);CHKERRQ(ierr);
2455     *d += rstart;
2456 
2457   }
2458   PetscFunctionReturn(0);
2459 }
2460 
2461 
2462 /* -------------------------------------------------------------------*/
2463 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2464                                        MatGetRow_MPIAIJ,
2465                                        MatRestoreRow_MPIAIJ,
2466                                        MatMult_MPIAIJ,
2467                                 /* 4*/ MatMultAdd_MPIAIJ,
2468                                        MatMultTranspose_MPIAIJ,
2469                                        MatMultTransposeAdd_MPIAIJ,
2470                                        0,
2471                                        0,
2472                                        0,
2473                                 /*10*/ 0,
2474                                        0,
2475                                        0,
2476                                        MatSOR_MPIAIJ,
2477                                        MatTranspose_MPIAIJ,
2478                                 /*15*/ MatGetInfo_MPIAIJ,
2479                                        MatEqual_MPIAIJ,
2480                                        MatGetDiagonal_MPIAIJ,
2481                                        MatDiagonalScale_MPIAIJ,
2482                                        MatNorm_MPIAIJ,
2483                                 /*20*/ MatAssemblyBegin_MPIAIJ,
2484                                        MatAssemblyEnd_MPIAIJ,
2485                                        MatSetOption_MPIAIJ,
2486                                        MatZeroEntries_MPIAIJ,
2487                                 /*24*/ MatZeroRows_MPIAIJ,
2488                                        0,
2489                                        0,
2490                                        0,
2491                                        0,
2492                                 /*29*/ MatSetUp_MPIAIJ,
2493                                        0,
2494                                        0,
2495                                        MatGetDiagonalBlock_MPIAIJ,
2496                                        0,
2497                                 /*34*/ MatDuplicate_MPIAIJ,
2498                                        0,
2499                                        0,
2500                                        0,
2501                                        0,
2502                                 /*39*/ MatAXPY_MPIAIJ,
2503                                        MatCreateSubMatrices_MPIAIJ,
2504                                        MatIncreaseOverlap_MPIAIJ,
2505                                        MatGetValues_MPIAIJ,
2506                                        MatCopy_MPIAIJ,
2507                                 /*44*/ MatGetRowMax_MPIAIJ,
2508                                        MatScale_MPIAIJ,
2509                                        MatShift_MPIAIJ,
2510                                        MatDiagonalSet_MPIAIJ,
2511                                        MatZeroRowsColumns_MPIAIJ,
2512                                 /*49*/ MatSetRandom_MPIAIJ,
2513                                        0,
2514                                        0,
2515                                        0,
2516                                        0,
2517                                 /*54*/ MatFDColoringCreate_MPIXAIJ,
2518                                        0,
2519                                        MatSetUnfactored_MPIAIJ,
2520                                        MatPermute_MPIAIJ,
2521                                        0,
2522                                 /*59*/ MatCreateSubMatrix_MPIAIJ,
2523                                        MatDestroy_MPIAIJ,
2524                                        MatView_MPIAIJ,
2525                                        0,
2526                                        MatMatMatMult_MPIAIJ_MPIAIJ_MPIAIJ,
2527                                 /*64*/ MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ,
2528                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2529                                        0,
2530                                        0,
2531                                        0,
2532                                 /*69*/ MatGetRowMaxAbs_MPIAIJ,
2533                                        MatGetRowMinAbs_MPIAIJ,
2534                                        0,
2535                                        0,
2536                                        0,
2537                                        0,
2538                                 /*75*/ MatFDColoringApply_AIJ,
2539                                        MatSetFromOptions_MPIAIJ,
2540                                        0,
2541                                        0,
2542                                        MatFindZeroDiagonals_MPIAIJ,
2543                                 /*80*/ 0,
2544                                        0,
2545                                        0,
2546                                 /*83*/ MatLoad_MPIAIJ,
2547                                        0,
2548                                        0,
2549                                        0,
2550                                        0,
2551                                        0,
2552                                 /*89*/ MatMatMult_MPIAIJ_MPIAIJ,
2553                                        MatMatMultSymbolic_MPIAIJ_MPIAIJ,
2554                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2555                                        MatPtAP_MPIAIJ_MPIAIJ,
2556                                        MatPtAPSymbolic_MPIAIJ_MPIAIJ,
2557                                 /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2558                                        0,
2559                                        0,
2560                                        0,
2561                                        0,
2562                                 /*99*/ 0,
2563                                        0,
2564                                        0,
2565                                        MatConjugate_MPIAIJ,
2566                                        0,
2567                                 /*104*/MatSetValuesRow_MPIAIJ,
2568                                        MatRealPart_MPIAIJ,
2569                                        MatImaginaryPart_MPIAIJ,
2570                                        0,
2571                                        0,
2572                                 /*109*/0,
2573                                        0,
2574                                        MatGetRowMin_MPIAIJ,
2575                                        0,
2576                                        MatMissingDiagonal_MPIAIJ,
2577                                 /*114*/MatGetSeqNonzeroStructure_MPIAIJ,
2578                                        0,
2579                                        MatGetGhosts_MPIAIJ,
2580                                        0,
2581                                        0,
2582                                 /*119*/0,
2583                                        0,
2584                                        0,
2585                                        0,
2586                                        MatGetMultiProcBlock_MPIAIJ,
2587                                 /*124*/MatFindNonzeroRows_MPIAIJ,
2588                                        MatGetColumnNorms_MPIAIJ,
2589                                        MatInvertBlockDiagonal_MPIAIJ,
2590                                        0,
2591                                        MatCreateSubMatricesMPI_MPIAIJ,
2592                                 /*129*/0,
2593                                        MatTransposeMatMult_MPIAIJ_MPIAIJ,
2594                                        MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ,
2595                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2596                                        0,
2597                                 /*134*/0,
2598                                        0,
2599                                        0,
2600                                        0,
2601                                        0,
2602                                 /*139*/MatSetBlockSizes_MPIAIJ,
2603                                        0,
2604                                        0,
2605                                        MatFDColoringSetUp_MPIXAIJ,
2606                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2607                                 /*144*/MatCreateMPIMatConcatenateSeqMat_MPIAIJ
2608 };
2609 
2610 /* ----------------------------------------------------------------------------------------*/
2611 
2612 PetscErrorCode  MatStoreValues_MPIAIJ(Mat mat)
2613 {
2614   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2615   PetscErrorCode ierr;
2616 
2617   PetscFunctionBegin;
2618   ierr = MatStoreValues(aij->A);CHKERRQ(ierr);
2619   ierr = MatStoreValues(aij->B);CHKERRQ(ierr);
2620   PetscFunctionReturn(0);
2621 }
2622 
2623 PetscErrorCode  MatRetrieveValues_MPIAIJ(Mat mat)
2624 {
2625   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
2626   PetscErrorCode ierr;
2627 
2628   PetscFunctionBegin;
2629   ierr = MatRetrieveValues(aij->A);CHKERRQ(ierr);
2630   ierr = MatRetrieveValues(aij->B);CHKERRQ(ierr);
2631   PetscFunctionReturn(0);
2632 }
2633 
2634 PetscErrorCode  MatMPIAIJSetPreallocation_MPIAIJ(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
2635 {
2636   Mat_MPIAIJ     *b;
2637   PetscErrorCode ierr;
2638 
2639   PetscFunctionBegin;
2640   ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
2641   ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
2642   b = (Mat_MPIAIJ*)B->data;
2643 
2644 #if defined(PETSC_USE_CTABLE)
2645   ierr = PetscTableDestroy(&b->colmap);CHKERRQ(ierr);
2646 #else
2647   ierr = PetscFree(b->colmap);CHKERRQ(ierr);
2648 #endif
2649   ierr = PetscFree(b->garray);CHKERRQ(ierr);
2650   ierr = VecDestroy(&b->lvec);CHKERRQ(ierr);
2651   ierr = VecScatterDestroy(&b->Mvctx);CHKERRQ(ierr);
2652 
2653   /* Because the B will have been resized we simply destroy it and create a new one each time */
2654   ierr = MatDestroy(&b->B);CHKERRQ(ierr);
2655   ierr = MatCreate(PETSC_COMM_SELF,&b->B);CHKERRQ(ierr);
2656   ierr = MatSetSizes(b->B,B->rmap->n,B->cmap->N,B->rmap->n,B->cmap->N);CHKERRQ(ierr);
2657   ierr = MatSetBlockSizesFromMats(b->B,B,B);CHKERRQ(ierr);
2658   ierr = MatSetType(b->B,MATSEQAIJ);CHKERRQ(ierr);
2659   ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->B);CHKERRQ(ierr);
2660 
2661   if (!B->preallocated) {
2662     ierr = MatCreate(PETSC_COMM_SELF,&b->A);CHKERRQ(ierr);
2663     ierr = MatSetSizes(b->A,B->rmap->n,B->cmap->n,B->rmap->n,B->cmap->n);CHKERRQ(ierr);
2664     ierr = MatSetBlockSizesFromMats(b->A,B,B);CHKERRQ(ierr);
2665     ierr = MatSetType(b->A,MATSEQAIJ);CHKERRQ(ierr);
2666     ierr = PetscLogObjectParent((PetscObject)B,(PetscObject)b->A);CHKERRQ(ierr);
2667   }
2668 
2669   ierr = MatSeqAIJSetPreallocation(b->A,d_nz,d_nnz);CHKERRQ(ierr);
2670   ierr = MatSeqAIJSetPreallocation(b->B,o_nz,o_nnz);CHKERRQ(ierr);
2671   B->preallocated  = PETSC_TRUE;
2672   B->was_assembled = PETSC_FALSE;
2673   B->assembled     = PETSC_FALSE;;
2674   PetscFunctionReturn(0);
2675 }
2676 
2677 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin,MatDuplicateOption cpvalues,Mat *newmat)
2678 {
2679   Mat            mat;
2680   Mat_MPIAIJ     *a,*oldmat = (Mat_MPIAIJ*)matin->data;
2681   PetscErrorCode ierr;
2682 
2683   PetscFunctionBegin;
2684   *newmat = 0;
2685   ierr    = MatCreate(PetscObjectComm((PetscObject)matin),&mat);CHKERRQ(ierr);
2686   ierr    = MatSetSizes(mat,matin->rmap->n,matin->cmap->n,matin->rmap->N,matin->cmap->N);CHKERRQ(ierr);
2687   ierr    = MatSetBlockSizesFromMats(mat,matin,matin);CHKERRQ(ierr);
2688   ierr    = MatSetType(mat,((PetscObject)matin)->type_name);CHKERRQ(ierr);
2689   ierr    = PetscMemcpy(mat->ops,matin->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
2690   a       = (Mat_MPIAIJ*)mat->data;
2691 
2692   mat->factortype   = matin->factortype;
2693   mat->assembled    = PETSC_TRUE;
2694   mat->insertmode   = NOT_SET_VALUES;
2695   mat->preallocated = PETSC_TRUE;
2696 
2697   a->size         = oldmat->size;
2698   a->rank         = oldmat->rank;
2699   a->donotstash   = oldmat->donotstash;
2700   a->roworiented  = oldmat->roworiented;
2701   a->rowindices   = 0;
2702   a->rowvalues    = 0;
2703   a->getrowactive = PETSC_FALSE;
2704 
2705   ierr = PetscLayoutReference(matin->rmap,&mat->rmap);CHKERRQ(ierr);
2706   ierr = PetscLayoutReference(matin->cmap,&mat->cmap);CHKERRQ(ierr);
2707 
2708   if (oldmat->colmap) {
2709 #if defined(PETSC_USE_CTABLE)
2710     ierr = PetscTableCreateCopy(oldmat->colmap,&a->colmap);CHKERRQ(ierr);
2711 #else
2712     ierr = PetscMalloc1(mat->cmap->N,&a->colmap);CHKERRQ(ierr);
2713     ierr = PetscLogObjectMemory((PetscObject)mat,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2714     ierr = PetscMemcpy(a->colmap,oldmat->colmap,(mat->cmap->N)*sizeof(PetscInt));CHKERRQ(ierr);
2715 #endif
2716   } else a->colmap = 0;
2717   if (oldmat->garray) {
2718     PetscInt len;
2719     len  = oldmat->B->cmap->n;
2720     ierr = PetscMalloc1(len+1,&a->garray);CHKERRQ(ierr);
2721     ierr = PetscLogObjectMemory((PetscObject)mat,len*sizeof(PetscInt));CHKERRQ(ierr);
2722     if (len) { ierr = PetscMemcpy(a->garray,oldmat->garray,len*sizeof(PetscInt));CHKERRQ(ierr); }
2723   } else a->garray = 0;
2724 
2725   ierr    = VecDuplicate(oldmat->lvec,&a->lvec);CHKERRQ(ierr);
2726   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->lvec);CHKERRQ(ierr);
2727   ierr    = VecScatterCopy(oldmat->Mvctx,&a->Mvctx);CHKERRQ(ierr);
2728   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->Mvctx);CHKERRQ(ierr);
2729   ierr    = MatDuplicate(oldmat->A,cpvalues,&a->A);CHKERRQ(ierr);
2730   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->A);CHKERRQ(ierr);
2731   ierr    = MatDuplicate(oldmat->B,cpvalues,&a->B);CHKERRQ(ierr);
2732   ierr    = PetscLogObjectParent((PetscObject)mat,(PetscObject)a->B);CHKERRQ(ierr);
2733   ierr    = PetscFunctionListDuplicate(((PetscObject)matin)->qlist,&((PetscObject)mat)->qlist);CHKERRQ(ierr);
2734   *newmat = mat;
2735   PetscFunctionReturn(0);
2736 }
2737 
2738 
2739 
2740 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
2741 {
2742   PetscScalar    *vals,*svals;
2743   MPI_Comm       comm;
2744   PetscErrorCode ierr;
2745   PetscMPIInt    rank,size,tag = ((PetscObject)viewer)->tag;
2746   PetscInt       i,nz,j,rstart,rend,mmax,maxnz = 0;
2747   PetscInt       header[4],*rowlengths = 0,M,N,m,*cols;
2748   PetscInt       *ourlens = NULL,*procsnz = NULL,*offlens = NULL,jj,*mycols,*smycols;
2749   PetscInt       cend,cstart,n,*rowners;
2750   int            fd;
2751   PetscInt       bs = newMat->rmap->bs;
2752 
2753   PetscFunctionBegin;
2754   /* force binary viewer to load .info file if it has not yet done so */
2755   ierr = PetscViewerSetUp(viewer);CHKERRQ(ierr);
2756   ierr = PetscObjectGetComm((PetscObject)viewer,&comm);CHKERRQ(ierr);
2757   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
2758   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
2759   ierr = PetscViewerBinaryGetDescriptor(viewer,&fd);CHKERRQ(ierr);
2760   if (!rank) {
2761     ierr = PetscBinaryRead(fd,(char*)header,4,PETSC_INT);CHKERRQ(ierr);
2762     if (header[0] != MAT_FILE_CLASSID) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"not matrix object");
2763     if (header[3] < 0) SETERRQ(PetscObjectComm((PetscObject)newMat),PETSC_ERR_FILE_UNEXPECTED,"Matrix stored in special format on disk,cannot load as MATMPIAIJ");
2764   }
2765 
2766   ierr = PetscOptionsBegin(comm,NULL,"Options for loading MATMPIAIJ matrix","Mat");CHKERRQ(ierr);
2767   ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
2768   ierr = PetscOptionsEnd();CHKERRQ(ierr);
2769   if (bs < 0) bs = 1;
2770 
2771   ierr = MPI_Bcast(header+1,3,MPIU_INT,0,comm);CHKERRQ(ierr);
2772   M    = header[1]; N = header[2];
2773 
2774   /* If global sizes are set, check if they are consistent with that given in the file */
2775   if (newMat->rmap->N >= 0 && newMat->rmap->N != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of rows:Matrix in file has (%D) and input matrix has (%D)",newMat->rmap->N,M);
2776   if (newMat->cmap->N >=0 && newMat->cmap->N != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED,"Inconsistent # of cols:Matrix in file has (%D) and input matrix has (%D)",newMat->cmap->N,N);
2777 
2778   /* determine ownership of all (block) rows */
2779   if (M%bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_FILE_UNEXPECTED, "Inconsistent # of rows (%d) and block size (%d)",M,bs);
2780   if (newMat->rmap->n < 0) m = bs*((M/bs)/size + (((M/bs) % size) > rank));    /* PETSC_DECIDE */
2781   else m = newMat->rmap->n; /* Set by user */
2782 
2783   ierr = PetscMalloc1(size+1,&rowners);CHKERRQ(ierr);
2784   ierr = MPI_Allgather(&m,1,MPIU_INT,rowners+1,1,MPIU_INT,comm);CHKERRQ(ierr);
2785 
2786   /* First process needs enough room for process with most rows */
2787   if (!rank) {
2788     mmax = rowners[1];
2789     for (i=2; i<=size; i++) {
2790       mmax = PetscMax(mmax, rowners[i]);
2791     }
2792   } else mmax = -1;             /* unused, but compilers complain */
2793 
2794   rowners[0] = 0;
2795   for (i=2; i<=size; i++) {
2796     rowners[i] += rowners[i-1];
2797   }
2798   rstart = rowners[rank];
2799   rend   = rowners[rank+1];
2800 
2801   /* distribute row lengths to all processors */
2802   ierr = PetscMalloc2(m,&ourlens,m,&offlens);CHKERRQ(ierr);
2803   if (!rank) {
2804     ierr = PetscBinaryRead(fd,ourlens,m,PETSC_INT);CHKERRQ(ierr);
2805     ierr = PetscMalloc1(mmax,&rowlengths);CHKERRQ(ierr);
2806     ierr = PetscCalloc1(size,&procsnz);CHKERRQ(ierr);
2807     for (j=0; j<m; j++) {
2808       procsnz[0] += ourlens[j];
2809     }
2810     for (i=1; i<size; i++) {
2811       ierr = PetscBinaryRead(fd,rowlengths,rowners[i+1]-rowners[i],PETSC_INT);CHKERRQ(ierr);
2812       /* calculate the number of nonzeros on each processor */
2813       for (j=0; j<rowners[i+1]-rowners[i]; j++) {
2814         procsnz[i] += rowlengths[j];
2815       }
2816       ierr = MPIULong_Send(rowlengths,rowners[i+1]-rowners[i],MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2817     }
2818     ierr = PetscFree(rowlengths);CHKERRQ(ierr);
2819   } else {
2820     ierr = MPIULong_Recv(ourlens,m,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2821   }
2822 
2823   if (!rank) {
2824     /* determine max buffer needed and allocate it */
2825     maxnz = 0;
2826     for (i=0; i<size; i++) {
2827       maxnz = PetscMax(maxnz,procsnz[i]);
2828     }
2829     ierr = PetscMalloc1(maxnz,&cols);CHKERRQ(ierr);
2830 
2831     /* read in my part of the matrix column indices  */
2832     nz   = procsnz[0];
2833     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2834     ierr = PetscBinaryRead(fd,mycols,nz,PETSC_INT);CHKERRQ(ierr);
2835 
2836     /* read in every one elses and ship off */
2837     for (i=1; i<size; i++) {
2838       nz   = procsnz[i];
2839       ierr = PetscBinaryRead(fd,cols,nz,PETSC_INT);CHKERRQ(ierr);
2840       ierr = MPIULong_Send(cols,nz,MPIU_INT,i,tag,comm);CHKERRQ(ierr);
2841     }
2842     ierr = PetscFree(cols);CHKERRQ(ierr);
2843   } else {
2844     /* determine buffer space needed for message */
2845     nz = 0;
2846     for (i=0; i<m; i++) {
2847       nz += ourlens[i];
2848     }
2849     ierr = PetscMalloc1(nz,&mycols);CHKERRQ(ierr);
2850 
2851     /* receive message of column indices*/
2852     ierr = MPIULong_Recv(mycols,nz,MPIU_INT,0,tag,comm);CHKERRQ(ierr);
2853   }
2854 
2855   /* determine column ownership if matrix is not square */
2856   if (N != M) {
2857     if (newMat->cmap->n < 0) n = N/size + ((N % size) > rank);
2858     else n = newMat->cmap->n;
2859     ierr   = MPI_Scan(&n,&cend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
2860     cstart = cend - n;
2861   } else {
2862     cstart = rstart;
2863     cend   = rend;
2864     n      = cend - cstart;
2865   }
2866 
2867   /* loop over local rows, determining number of off diagonal entries */
2868   ierr = PetscMemzero(offlens,m*sizeof(PetscInt));CHKERRQ(ierr);
2869   jj   = 0;
2870   for (i=0; i<m; i++) {
2871     for (j=0; j<ourlens[i]; j++) {
2872       if (mycols[jj] < cstart || mycols[jj] >= cend) offlens[i]++;
2873       jj++;
2874     }
2875   }
2876 
2877   for (i=0; i<m; i++) {
2878     ourlens[i] -= offlens[i];
2879   }
2880   ierr = MatSetSizes(newMat,m,n,M,N);CHKERRQ(ierr);
2881 
2882   if (bs > 1) {ierr = MatSetBlockSize(newMat,bs);CHKERRQ(ierr);}
2883 
2884   ierr = MatMPIAIJSetPreallocation(newMat,0,ourlens,0,offlens);CHKERRQ(ierr);
2885 
2886   for (i=0; i<m; i++) {
2887     ourlens[i] += offlens[i];
2888   }
2889 
2890   if (!rank) {
2891     ierr = PetscMalloc1(maxnz+1,&vals);CHKERRQ(ierr);
2892 
2893     /* read in my part of the matrix numerical values  */
2894     nz   = procsnz[0];
2895     ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2896 
2897     /* insert into matrix */
2898     jj      = rstart;
2899     smycols = mycols;
2900     svals   = vals;
2901     for (i=0; i<m; i++) {
2902       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2903       smycols += ourlens[i];
2904       svals   += ourlens[i];
2905       jj++;
2906     }
2907 
2908     /* read in other processors and ship out */
2909     for (i=1; i<size; i++) {
2910       nz   = procsnz[i];
2911       ierr = PetscBinaryRead(fd,vals,nz,PETSC_SCALAR);CHKERRQ(ierr);
2912       ierr = MPIULong_Send(vals,nz,MPIU_SCALAR,i,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2913     }
2914     ierr = PetscFree(procsnz);CHKERRQ(ierr);
2915   } else {
2916     /* receive numeric values */
2917     ierr = PetscMalloc1(nz+1,&vals);CHKERRQ(ierr);
2918 
2919     /* receive message of values*/
2920     ierr = MPIULong_Recv(vals,nz,MPIU_SCALAR,0,((PetscObject)newMat)->tag,comm);CHKERRQ(ierr);
2921 
2922     /* insert into matrix */
2923     jj      = rstart;
2924     smycols = mycols;
2925     svals   = vals;
2926     for (i=0; i<m; i++) {
2927       ierr     = MatSetValues_MPIAIJ(newMat,1,&jj,ourlens[i],smycols,svals,INSERT_VALUES);CHKERRQ(ierr);
2928       smycols += ourlens[i];
2929       svals   += ourlens[i];
2930       jj++;
2931     }
2932   }
2933   ierr = PetscFree2(ourlens,offlens);CHKERRQ(ierr);
2934   ierr = PetscFree(vals);CHKERRQ(ierr);
2935   ierr = PetscFree(mycols);CHKERRQ(ierr);
2936   ierr = PetscFree(rowners);CHKERRQ(ierr);
2937   ierr = MatAssemblyBegin(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2938   ierr = MatAssemblyEnd(newMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
2939   PetscFunctionReturn(0);
2940 }
2941 
2942 /* TODO: Not scalable because of ISAllGather() unless getting all columns. */
2943 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat,IS isrow,IS iscol,MatReuse call,Mat *newmat)
2944 {
2945   PetscErrorCode ierr;
2946   IS             iscol_local;
2947   PetscInt       csize;
2948 
2949   PetscFunctionBegin;
2950   ierr = ISGetLocalSize(iscol,&csize);CHKERRQ(ierr);
2951   if (call == MAT_REUSE_MATRIX) {
2952     ierr = PetscObjectQuery((PetscObject)*newmat,"ISAllGather",(PetscObject*)&iscol_local);CHKERRQ(ierr);
2953     if (!iscol_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
2954   } else {
2955     /* check if we are grabbing all columns*/
2956     PetscBool    isstride;
2957     PetscMPIInt  lisstride = 0,gisstride;
2958     ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&isstride);CHKERRQ(ierr);
2959     if (isstride) {
2960       PetscInt  start,len,mstart,mlen;
2961       ierr = ISStrideGetInfo(iscol,&start,NULL);CHKERRQ(ierr);
2962       ierr = ISGetLocalSize(iscol,&len);CHKERRQ(ierr);
2963       ierr = MatGetOwnershipRangeColumn(mat,&mstart,&mlen);CHKERRQ(ierr);
2964       if (mstart == start && mlen-mstart == len) lisstride = 1;
2965     }
2966     ierr = MPIU_Allreduce(&lisstride,&gisstride,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
2967     if (gisstride) {
2968       PetscInt N;
2969       ierr = MatGetSize(mat,NULL,&N);CHKERRQ(ierr);
2970       ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),N,0,1,&iscol_local);CHKERRQ(ierr);
2971       ierr = ISSetIdentity(iscol_local);CHKERRQ(ierr);
2972       ierr = PetscInfo(mat,"Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n");CHKERRQ(ierr);
2973     } else {
2974       PetscInt cbs;
2975       ierr = ISGetBlockSize(iscol,&cbs);CHKERRQ(ierr);
2976       ierr = ISAllGather(iscol,&iscol_local);CHKERRQ(ierr);
2977       ierr = ISSetBlockSize(iscol_local,cbs);CHKERRQ(ierr);
2978     }
2979   }
2980 
2981   ierr = MatCreateSubMatrix_MPIAIJ_Private(mat,isrow,iscol_local,csize,call,newmat);CHKERRQ(ierr);
2982   if (call == MAT_INITIAL_MATRIX) {
2983     ierr = PetscObjectCompose((PetscObject)*newmat,"ISAllGather",(PetscObject)iscol_local);CHKERRQ(ierr);
2984     ierr = ISDestroy(&iscol_local);CHKERRQ(ierr);
2985   }
2986   PetscFunctionReturn(0);
2987 }
2988 
2989 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat*);
2990 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat,PetscInt,const IS[],const IS[],MatReuse,PetscBool,Mat*);
2991 
2992 PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private_SameDist(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
2993 {
2994   PetscErrorCode ierr;
2995   PetscInt       i,m,n,rstart,row,rend,nz,j,bs,cbs;
2996   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
2997   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)mat->data;
2998   Mat            M,Msub,B=a->B;
2999   MatScalar      *aa;
3000   Mat_SeqAIJ     *aij;
3001   PetscInt       *garray = a->garray,*colsub;
3002   PetscInt       count,Bn=B->cmap->N,cstart=mat->cmap->rstart,cend=mat->cmap->rend;
3003   IS             iscol_sub,iscmap;
3004   const PetscInt *is_idx,*cmap;
3005 
3006   PetscFunctionBegin;
3007   ierr = ISGetLocalSize(iscol,&n);CHKERRQ(ierr); /* iscol should be sequential */
3008 
3009   if (call == MAT_INITIAL_MATRIX) {
3010     /* create scalable iscol_sub (a subset of iscol) */
3011     PetscInt *idx,*cmap1;
3012 
3013     ierr = PetscMalloc2(n,&idx,n,&cmap1);CHKERRQ(ierr);
3014     ierr = ISGetIndices(iscol,&is_idx);CHKERRQ(ierr);
3015     count = 0;
3016 
3017     /* A part */
3018     j = cstart;
3019     for (i=0; i<n; i++) {
3020       if (j >= cend) break;
3021       if (is_idx[i] == j) {
3022         idx[count]  = j;
3023         cmap1[count] = i; /* column index in submat */
3024         count++; j++;
3025       } else if (is_idx[i] > j) {
3026         while (is_idx[i] > j && j < cend-1) j++;
3027         if (is_idx[i] == j) {
3028           idx[count]  = j;
3029           cmap1[count] = i; /* column index in submat */
3030           count++; j++;
3031         }
3032       }
3033     }
3034 
3035     /* B part */
3036     j = 0;
3037     for (i=0; i<n; i++) {
3038       if (j >= Bn) break;
3039       if (is_idx[i] == garray[j]) {
3040         idx[count]  = garray[j];
3041         cmap1[count] = i;  /* column index in submat */
3042         count++; j++;
3043       } else if (is_idx[i] > garray[j]) {
3044         while (is_idx[i] > garray[j] && j < Bn-1) j++;
3045         if (is_idx[i] == garray[j]) {
3046           idx[count]  = garray[j];
3047           cmap1[count] = i; /* column index in submat */
3048           count++; j++;
3049         }
3050       }
3051     }
3052     ierr = PetscSortInt(count,cmap1);CHKERRQ(ierr);
3053     ierr = ISRestoreIndices(iscol,&is_idx);CHKERRQ(ierr);
3054 
3055     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol),count,idx,PETSC_COPY_VALUES,&iscol_sub);CHKERRQ(ierr);
3056     ierr = ISSort(iscol_sub);CHKERRQ(ierr);
3057 
3058     ierr = ISCreateGeneral(PetscObjectComm((PetscObject)iscol),count,cmap1,PETSC_COPY_VALUES,&iscmap);CHKERRQ(ierr);
3059     ierr = PetscFree2(idx,cmap1);CHKERRQ(ierr);
3060 
3061     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_INITIAL_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3062 
3063   } else { /* call ==  MAT_REUSE_MATRIX */
3064     ierr = PetscObjectQuery((PetscObject)*newmat,"SubIScol",(PetscObject*)&iscol_sub);CHKERRQ(ierr);
3065     if (!iscol_sub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"SubIScol passed in was not used before, cannot reuse");
3066     ierr = ISGetLocalSize(iscol_sub,&count);CHKERRQ(ierr);
3067 
3068     ierr = PetscObjectQuery((PetscObject)*newmat,"Subcmap",(PetscObject*)&iscmap);CHKERRQ(ierr);
3069     if (!iscmap) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcmap passed in was not used before, cannot reuse");
3070 
3071     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Msub);CHKERRQ(ierr);
3072     if (!Msub) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3073 
3074     ierr = MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat,1,&isrow,&iscol_sub,MAT_REUSE_MATRIX,PETSC_FALSE,&Msub);CHKERRQ(ierr);
3075   }
3076 
3077   aij = (Mat_SeqAIJ*)(Msub)->data;
3078   ii  = aij->i;
3079   ierr = ISGetIndices(iscmap,&cmap);CHKERRQ(ierr);
3080 
3081   /*
3082       m - number of local rows
3083       n - number of columns (same on all processors)
3084       rstart - first row in new global matrix generated
3085   */
3086   ierr = MatGetSize(Msub,&m,NULL);CHKERRQ(ierr);
3087 
3088   if (call == MAT_INITIAL_MATRIX) {
3089     MPI_Comm       comm;
3090     PetscMPIInt    rank,size;
3091 
3092     ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3093     ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3094     ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3095 
3096     /*
3097         Determine the number of non-zeros in the diagonal and off-diagonal
3098         portions of the matrix in order to do correct preallocation
3099     */
3100 
3101     /* first get start and end of "diagonal" columns */
3102     if (csize == PETSC_DECIDE) {
3103       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3104       if (mglobal == n) { /* square matrix */
3105         nlocal = m;
3106       } else {
3107         nlocal = n/size + ((n % size) > rank);
3108       }
3109     } else {
3110       nlocal = csize;
3111     }
3112     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3113     rstart = rend - nlocal;
3114     if (rank == size - 1 && rend != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %D do not add up to total number of columns %D",rend,n);
3115 
3116     /* next, compute all the lengths */
3117     jj    = aij->j;
3118     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3119     olens = dlens + m;
3120     for (i=0; i<m; i++) {
3121       jend = ii[i+1] - ii[i];
3122       olen = 0;
3123       dlen = 0;
3124       for (j=0; j<jend; j++) {
3125         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3126         else dlen++;
3127         jj++;
3128       }
3129       olens[i] = olen;
3130       dlens[i] = dlen;
3131     }
3132     ierr = MatGetBlockSizes(Msub,&bs,&cbs);CHKERRQ(ierr);
3133 
3134     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3135     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3136     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3137     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3138     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3139     ierr = PetscFree(dlens);CHKERRQ(ierr);
3140   } else {
3141     M    = *newmat;
3142     ierr = MatGetLocalSize(M,&i,NULL);CHKERRQ(ierr);
3143     if (i != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3144     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3145     /*
3146          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3147        rather than the slower MatSetValues().
3148     */
3149     M->was_assembled = PETSC_TRUE;
3150     M->assembled     = PETSC_FALSE;
3151   }
3152 
3153   /* set values of Msub to *newmat */
3154   ierr = PetscMalloc1(count,&colsub);CHKERRQ(ierr);
3155   ierr = MatGetOwnershipRange(M,&rstart,NULL);CHKERRQ(ierr);
3156 
3157   jj   = aij->j;
3158   aa   = aij->a;
3159   for (i=0; i<m; i++) {
3160     row = rstart + i;
3161     nz  = ii[i+1] - ii[i];
3162     for (j=0; j<nz; j++) colsub[j] = cmap[jj[j]];
3163     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,colsub,aa,INSERT_VALUES);CHKERRQ(ierr);
3164     jj += nz; aa += nz;
3165   }
3166   ierr = ISRestoreIndices(iscmap,&cmap);CHKERRQ(ierr);
3167 
3168   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3169   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3170   *newmat = M;
3171 
3172   ierr = PetscFree(colsub);CHKERRQ(ierr);
3173 
3174   /* save Msub, iscol_sub and iscmap used in processor for next request */
3175   if (call ==  MAT_INITIAL_MATRIX) {
3176     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Msub);CHKERRQ(ierr);
3177     ierr = MatDestroy(&Msub);CHKERRQ(ierr);
3178 
3179     ierr = PetscObjectCompose((PetscObject)M,"SubIScol",(PetscObject)iscol_sub);CHKERRQ(ierr);
3180     ierr = ISDestroy(&iscol_sub);CHKERRQ(ierr);
3181 
3182     ierr = PetscObjectCompose((PetscObject)M,"Subcmap",(PetscObject)iscmap);CHKERRQ(ierr);
3183     ierr = ISDestroy(&iscmap);CHKERRQ(ierr);
3184   }
3185   PetscFunctionReturn(0);
3186 }
3187 
3188 /*
3189     Not great since it makes two copies of the submatrix, first an SeqAIJ
3190   in local and then by concatenating the local matrices the end result.
3191   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3192 
3193   Note: This requires a sequential iscol with all indices.
3194 */
3195 PetscErrorCode MatCreateSubMatrix_MPIAIJ_Private(Mat mat,IS isrow,IS iscol,PetscInt csize,MatReuse call,Mat *newmat)
3196 {
3197   PetscErrorCode ierr;
3198   PetscMPIInt    rank,size;
3199   PetscInt       i,m,n,rstart,row,rend,nz,*cwork,j,bs,cbs;
3200   PetscInt       *ii,*jj,nlocal,*dlens,*olens,dlen,olen,jend,mglobal;
3201   Mat            M,Mreuse;
3202   MatScalar      *aa,*vwork;
3203   MPI_Comm       comm;
3204   Mat_SeqAIJ     *aij;
3205   PetscBool      sameDist=PETSC_FALSE,tsameDist;
3206 
3207   PetscFunctionBegin;
3208   ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
3209   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
3210   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3211 
3212   /* If isrow has same processor distribution as mat, then use a scalable routine */
3213   ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
3214   if (!n) {
3215     sameDist=PETSC_TRUE;
3216   } else {
3217     ierr = ISGetMinMax(isrow,&i,&j);CHKERRQ(ierr);
3218     ierr = MatGetOwnershipRange(mat,&rstart,&rend);CHKERRQ(ierr);
3219     if (i >= rstart && j < rend) sameDist=PETSC_TRUE;
3220   }
3221   ierr = MPIU_Allreduce(&sameDist,&tsameDist,1,MPIU_BOOL,MPI_LAND,comm);CHKERRQ(ierr);
3222   if (tsameDist) {
3223     ierr = MatCreateSubMatrix_MPIAIJ_Private_SameDist(mat,isrow,iscol,csize,call,newmat);CHKERRQ(ierr);
3224     PetscFunctionReturn(0);
3225   }
3226 
3227   if (call ==  MAT_REUSE_MATRIX) {
3228     ierr = PetscObjectQuery((PetscObject)*newmat,"SubMatrix",(PetscObject*)&Mreuse);CHKERRQ(ierr);
3229     if (!Mreuse) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Submatrix passed in was not used before, cannot reuse");
3230     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_REUSE_MATRIX,&Mreuse);CHKERRQ(ierr);
3231   } else {
3232     ierr = MatCreateSubMatrices_MPIAIJ_Local(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&Mreuse);CHKERRQ(ierr);
3233   }
3234 
3235   /*
3236       m - number of local rows
3237       n - number of columns (same on all processors)
3238       rstart - first row in new global matrix generated
3239   */
3240   ierr = MatGetSize(Mreuse,&m,&n);CHKERRQ(ierr);
3241   ierr = MatGetBlockSizes(Mreuse,&bs,&cbs);CHKERRQ(ierr);
3242   if (call == MAT_INITIAL_MATRIX) {
3243     aij = (Mat_SeqAIJ*)(Mreuse)->data;
3244     ii  = aij->i;
3245     jj  = aij->j;
3246 
3247     /*
3248         Determine the number of non-zeros in the diagonal and off-diagonal
3249         portions of the matrix in order to do correct preallocation
3250     */
3251 
3252     /* first get start and end of "diagonal" columns */
3253     if (csize == PETSC_DECIDE) {
3254       ierr = ISGetSize(isrow,&mglobal);CHKERRQ(ierr);
3255       if (mglobal == n) { /* square matrix */
3256         nlocal = m;
3257       } else {
3258         nlocal = n/size + ((n % size) > rank);
3259       }
3260     } else {
3261       nlocal = csize;
3262     }
3263     ierr   = MPI_Scan(&nlocal,&rend,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3264     rstart = rend - nlocal;
3265     if (rank == size - 1 && rend != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Local column sizes %D do not add up to total number of columns %D",rend,n);
3266 
3267     /* next, compute all the lengths */
3268     ierr  = PetscMalloc1(2*m+1,&dlens);CHKERRQ(ierr);
3269     olens = dlens + m;
3270     for (i=0; i<m; i++) {
3271       jend = ii[i+1] - ii[i];
3272       olen = 0;
3273       dlen = 0;
3274       for (j=0; j<jend; j++) {
3275         if (*jj < rstart || *jj >= rend) olen++;
3276         else dlen++;
3277         jj++;
3278       }
3279       olens[i] = olen;
3280       dlens[i] = dlen;
3281     }
3282     ierr = MatCreate(comm,&M);CHKERRQ(ierr);
3283     ierr = MatSetSizes(M,m,nlocal,PETSC_DECIDE,n);CHKERRQ(ierr);
3284     ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr);
3285     ierr = MatSetType(M,((PetscObject)mat)->type_name);CHKERRQ(ierr);
3286     ierr = MatMPIAIJSetPreallocation(M,0,dlens,0,olens);CHKERRQ(ierr);
3287     ierr = PetscFree(dlens);CHKERRQ(ierr);
3288   } else {
3289     PetscInt ml,nl;
3290 
3291     M    = *newmat;
3292     ierr = MatGetLocalSize(M,&ml,&nl);CHKERRQ(ierr);
3293     if (ml != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Previous matrix must be same size/layout as request");
3294     ierr = MatZeroEntries(M);CHKERRQ(ierr);
3295     /*
3296          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3297        rather than the slower MatSetValues().
3298     */
3299     M->was_assembled = PETSC_TRUE;
3300     M->assembled     = PETSC_FALSE;
3301   }
3302   ierr = MatGetOwnershipRange(M,&rstart,&rend);CHKERRQ(ierr);
3303   aij  = (Mat_SeqAIJ*)(Mreuse)->data;
3304   ii   = aij->i;
3305   jj   = aij->j;
3306   aa   = aij->a;
3307   for (i=0; i<m; i++) {
3308     row   = rstart + i;
3309     nz    = ii[i+1] - ii[i];
3310     cwork = jj;     jj += nz;
3311     vwork = aa;     aa += nz;
3312     ierr  = MatSetValues_MPIAIJ(M,1,&row,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
3313   }
3314 
3315   ierr    = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3316   ierr    = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3317   *newmat = M;
3318 
3319   /* save submatrix used in processor for next request */
3320   if (call ==  MAT_INITIAL_MATRIX) {
3321     ierr = PetscObjectCompose((PetscObject)M,"SubMatrix",(PetscObject)Mreuse);CHKERRQ(ierr);
3322     ierr = MatDestroy(&Mreuse);CHKERRQ(ierr);
3323   }
3324   PetscFunctionReturn(0);
3325 }
3326 
3327 PetscErrorCode  MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B,const PetscInt Ii[],const PetscInt J[],const PetscScalar v[])
3328 {
3329   PetscInt       m,cstart, cend,j,nnz,i,d;
3330   PetscInt       *d_nnz,*o_nnz,nnz_max = 0,rstart,ii;
3331   const PetscInt *JJ;
3332   PetscScalar    *values;
3333   PetscErrorCode ierr;
3334   PetscBool      nooffprocentries;
3335 
3336   PetscFunctionBegin;
3337   if (Ii[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Ii[0] must be 0 it is %D",Ii[0]);
3338 
3339   ierr   = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
3340   ierr   = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
3341   m      = B->rmap->n;
3342   cstart = B->cmap->rstart;
3343   cend   = B->cmap->rend;
3344   rstart = B->rmap->rstart;
3345 
3346   ierr = PetscMalloc2(m,&d_nnz,m,&o_nnz);CHKERRQ(ierr);
3347 
3348 #if defined(PETSC_USE_DEBUGGING)
3349   for (i=0; i<m; i++) {
3350     nnz = Ii[i+1]- Ii[i];
3351     JJ  = J + Ii[i];
3352     if (nnz < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local row %D has a negative %D number of columns",i,nnz);
3353     if (nnz && (JJ[0] < 0)) SETERRRQ1(PETSC_ERR_ARG_WRONGSTATE,"Row %D starts with negative column index",i,j);
3354     if (nnz && (JJ[nnz-1] >= B->cmap->N) SETERRRQ3(PETSC_ERR_ARG_WRONGSTATE,"Row %D ends with too large a column index %D (max allowed %D)",i,JJ[nnz-1],B->cmap->N);
3355   }
3356 #endif
3357 
3358   for (i=0; i<m; i++) {
3359     nnz     = Ii[i+1]- Ii[i];
3360     JJ      = J + Ii[i];
3361     nnz_max = PetscMax(nnz_max,nnz);
3362     d       = 0;
3363     for (j=0; j<nnz; j++) {
3364       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3365     }
3366     d_nnz[i] = d;
3367     o_nnz[i] = nnz - d;
3368   }
3369   ierr = MatMPIAIJSetPreallocation(B,0,d_nnz,0,o_nnz);CHKERRQ(ierr);
3370   ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
3371 
3372   if (v) values = (PetscScalar*)v;
3373   else {
3374     ierr = PetscCalloc1(nnz_max+1,&values);CHKERRQ(ierr);
3375   }
3376 
3377   for (i=0; i<m; i++) {
3378     ii   = i + rstart;
3379     nnz  = Ii[i+1]- Ii[i];
3380     ierr = MatSetValues_MPIAIJ(B,1,&ii,nnz,J+Ii[i],values+(v ? Ii[i] : 0),INSERT_VALUES);CHKERRQ(ierr);
3381   }
3382   nooffprocentries    = B->nooffprocentries;
3383   B->nooffprocentries = PETSC_TRUE;
3384   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3385   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3386   B->nooffprocentries = nooffprocentries;
3387 
3388   if (!v) {
3389     ierr = PetscFree(values);CHKERRQ(ierr);
3390   }
3391   ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
3392   PetscFunctionReturn(0);
3393 }
3394 
3395 /*@
3396    MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in AIJ format
3397    (the default parallel PETSc format).
3398 
3399    Collective on MPI_Comm
3400 
3401    Input Parameters:
3402 +  B - the matrix
3403 .  i - the indices into j for the start of each local row (starts with zero)
3404 .  j - the column indices for each local row (starts with zero)
3405 -  v - optional values in the matrix
3406 
3407    Level: developer
3408 
3409    Notes:
3410        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3411      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3412      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3413 
3414        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3415 
3416        The format which is used for the sparse matrix input, is equivalent to a
3417     row-major ordering.. i.e for the following matrix, the input data expected is
3418     as shown
3419 
3420 $        1 0 0
3421 $        2 0 3     P0
3422 $       -------
3423 $        4 5 6     P1
3424 $
3425 $     Process0 [P0]: rows_owned=[0,1]
3426 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3427 $        j =  {0,0,2}  [size = 3]
3428 $        v =  {1,2,3}  [size = 3]
3429 $
3430 $     Process1 [P1]: rows_owned=[2]
3431 $        i =  {0,3}    [size = nrow+1  = 1+1]
3432 $        j =  {0,1,2}  [size = 3]
3433 $        v =  {4,5,6}  [size = 3]
3434 
3435 .keywords: matrix, aij, compressed row, sparse, parallel
3436 
3437 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatCreateAIJ(), MATMPIAIJ,
3438           MatCreateSeqAIJWithArrays(), MatCreateMPIAIJWithSplitArrays()
3439 @*/
3440 PetscErrorCode  MatMPIAIJSetPreallocationCSR(Mat B,const PetscInt i[],const PetscInt j[], const PetscScalar v[])
3441 {
3442   PetscErrorCode ierr;
3443 
3444   PetscFunctionBegin;
3445   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocationCSR_C",(Mat,const PetscInt[],const PetscInt[],const PetscScalar[]),(B,i,j,v));CHKERRQ(ierr);
3446   PetscFunctionReturn(0);
3447 }
3448 
3449 /*@C
3450    MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in AIJ format
3451    (the default parallel PETSc format).  For good matrix assembly performance
3452    the user should preallocate the matrix storage by setting the parameters
3453    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3454    performance can be increased by more than a factor of 50.
3455 
3456    Collective on MPI_Comm
3457 
3458    Input Parameters:
3459 +  B - the matrix
3460 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3461            (same value is used for all local rows)
3462 .  d_nnz - array containing the number of nonzeros in the various rows of the
3463            DIAGONAL portion of the local submatrix (possibly different for each row)
3464            or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure.
3465            The size of this array is equal to the number of local rows, i.e 'm'.
3466            For matrices that will be factored, you must leave room for (and set)
3467            the diagonal entry even if it is zero.
3468 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3469            submatrix (same value is used for all local rows).
3470 -  o_nnz - array containing the number of nonzeros in the various rows of the
3471            OFF-DIAGONAL portion of the local submatrix (possibly different for
3472            each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero
3473            structure. The size of this array is equal to the number
3474            of local rows, i.e 'm'.
3475 
3476    If the *_nnz parameter is given then the *_nz parameter is ignored
3477 
3478    The AIJ format (also called the Yale sparse matrix format or
3479    compressed row storage (CSR)), is fully compatible with standard Fortran 77
3480    storage.  The stored row and column indices begin with zero.
3481    See Users-Manual: ch_mat for details.
3482 
3483    The parallel matrix is partitioned such that the first m0 rows belong to
3484    process 0, the next m1 rows belong to process 1, the next m2 rows belong
3485    to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
3486 
3487    The DIAGONAL portion of the local submatrix of a processor can be defined
3488    as the submatrix which is obtained by extraction the part corresponding to
3489    the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
3490    first row that belongs to the processor, r2 is the last row belonging to
3491    the this processor, and c1-c2 is range of indices of the local part of a
3492    vector suitable for applying the matrix to.  This is an mxn matrix.  In the
3493    common case of a square matrix, the row and column ranges are the same and
3494    the DIAGONAL part is also square. The remaining portion of the local
3495    submatrix (mxN) constitute the OFF-DIAGONAL portion.
3496 
3497    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3498 
3499    You can call MatGetInfo() to get information on how effective the preallocation was;
3500    for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
3501    You can also run with the option -info and look for messages with the string
3502    malloc in them to see if additional memory allocation was needed.
3503 
3504    Example usage:
3505 
3506    Consider the following 8x8 matrix with 34 non-zero values, that is
3507    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3508    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3509    as follows:
3510 
3511 .vb
3512             1  2  0  |  0  3  0  |  0  4
3513     Proc0   0  5  6  |  7  0  0  |  8  0
3514             9  0 10  | 11  0  0  | 12  0
3515     -------------------------------------
3516            13  0 14  | 15 16 17  |  0  0
3517     Proc1   0 18  0  | 19 20 21  |  0  0
3518             0  0  0  | 22 23  0  | 24  0
3519     -------------------------------------
3520     Proc2  25 26 27  |  0  0 28  | 29  0
3521            30  0  0  | 31 32 33  |  0 34
3522 .ve
3523 
3524    This can be represented as a collection of submatrices as:
3525 
3526 .vb
3527       A B C
3528       D E F
3529       G H I
3530 .ve
3531 
3532    Where the submatrices A,B,C are owned by proc0, D,E,F are
3533    owned by proc1, G,H,I are owned by proc2.
3534 
3535    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3536    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3537    The 'M','N' parameters are 8,8, and have the same values on all procs.
3538 
3539    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3540    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3541    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3542    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3543    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3544    matrix, ans [DF] as another SeqAIJ matrix.
3545 
3546    When d_nz, o_nz parameters are specified, d_nz storage elements are
3547    allocated for every row of the local diagonal submatrix, and o_nz
3548    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3549    One way to choose d_nz and o_nz is to use the max nonzerors per local
3550    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3551    In this case, the values of d_nz,o_nz are:
3552 .vb
3553      proc0 : dnz = 2, o_nz = 2
3554      proc1 : dnz = 3, o_nz = 2
3555      proc2 : dnz = 1, o_nz = 4
3556 .ve
3557    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3558    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3559    for proc3. i.e we are using 12+15+10=37 storage locations to store
3560    34 values.
3561 
3562    When d_nnz, o_nnz parameters are specified, the storage is specified
3563    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3564    In the above case the values for d_nnz,o_nnz are:
3565 .vb
3566      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3567      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3568      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3569 .ve
3570    Here the space allocated is sum of all the above values i.e 34, and
3571    hence pre-allocation is perfect.
3572 
3573    Level: intermediate
3574 
3575 .keywords: matrix, aij, compressed row, sparse, parallel
3576 
3577 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateAIJ(), MatMPIAIJSetPreallocationCSR(),
3578           MATMPIAIJ, MatGetInfo(), PetscSplitOwnership()
3579 @*/
3580 PetscErrorCode  MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])
3581 {
3582   PetscErrorCode ierr;
3583 
3584   PetscFunctionBegin;
3585   PetscValidHeaderSpecific(B,MAT_CLASSID,1);
3586   PetscValidType(B,1);
3587   ierr = PetscTryMethod(B,"MatMPIAIJSetPreallocation_C",(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[]),(B,d_nz,d_nnz,o_nz,o_nnz));CHKERRQ(ierr);
3588   PetscFunctionReturn(0);
3589 }
3590 
3591 /*@
3592      MatCreateMPIAIJWithArrays - creates a MPI AIJ matrix using arrays that contain in standard
3593          CSR format the local rows.
3594 
3595    Collective on MPI_Comm
3596 
3597    Input Parameters:
3598 +  comm - MPI communicator
3599 .  m - number of local rows (Cannot be PETSC_DECIDE)
3600 .  n - This value should be the same as the local size used in creating the
3601        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3602        calculated if N is given) For square matrices n is almost always m.
3603 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3604 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3605 .   i - row indices
3606 .   j - column indices
3607 -   a - matrix values
3608 
3609    Output Parameter:
3610 .   mat - the matrix
3611 
3612    Level: intermediate
3613 
3614    Notes:
3615        The i, j, and a arrays ARE copied by this routine into the internal format used by PETSc;
3616      thus you CANNOT change the matrix entries by changing the values of a[] after you have
3617      called this routine. Use MatCreateMPIAIJWithSplitArrays() to avoid needing to copy the arrays.
3618 
3619        The i and j indices are 0 based, and i indices are indices corresponding to the local j array.
3620 
3621        The format which is used for the sparse matrix input, is equivalent to a
3622     row-major ordering.. i.e for the following matrix, the input data expected is
3623     as shown
3624 
3625 $        1 0 0
3626 $        2 0 3     P0
3627 $       -------
3628 $        4 5 6     P1
3629 $
3630 $     Process0 [P0]: rows_owned=[0,1]
3631 $        i =  {0,1,3}  [size = nrow+1  = 2+1]
3632 $        j =  {0,0,2}  [size = 3]
3633 $        v =  {1,2,3}  [size = 3]
3634 $
3635 $     Process1 [P1]: rows_owned=[2]
3636 $        i =  {0,3}    [size = nrow+1  = 1+1]
3637 $        j =  {0,1,2}  [size = 3]
3638 $        v =  {4,5,6}  [size = 3]
3639 
3640 .keywords: matrix, aij, compressed row, sparse, parallel
3641 
3642 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3643           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithSplitArrays()
3644 @*/
3645 PetscErrorCode  MatCreateMPIAIJWithArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt i[],const PetscInt j[],const PetscScalar a[],Mat *mat)
3646 {
3647   PetscErrorCode ierr;
3648 
3649   PetscFunctionBegin;
3650   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
3651   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
3652   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
3653   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
3654   /* ierr = MatSetBlockSizes(M,bs,cbs);CHKERRQ(ierr); */
3655   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
3656   ierr = MatMPIAIJSetPreallocationCSR(*mat,i,j,a);CHKERRQ(ierr);
3657   PetscFunctionReturn(0);
3658 }
3659 
3660 /*@C
3661    MatCreateAIJ - Creates a sparse parallel matrix in AIJ format
3662    (the default parallel PETSc format).  For good matrix assembly performance
3663    the user should preallocate the matrix storage by setting the parameters
3664    d_nz (or d_nnz) and o_nz (or o_nnz).  By setting these parameters accurately,
3665    performance can be increased by more than a factor of 50.
3666 
3667    Collective on MPI_Comm
3668 
3669    Input Parameters:
3670 +  comm - MPI communicator
3671 .  m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
3672            This value should be the same as the local size used in creating the
3673            y vector for the matrix-vector product y = Ax.
3674 .  n - This value should be the same as the local size used in creating the
3675        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
3676        calculated if N is given) For square matrices n is almost always m.
3677 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
3678 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
3679 .  d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
3680            (same value is used for all local rows)
3681 .  d_nnz - array containing the number of nonzeros in the various rows of the
3682            DIAGONAL portion of the local submatrix (possibly different for each row)
3683            or NULL, if d_nz is used to specify the nonzero structure.
3684            The size of this array is equal to the number of local rows, i.e 'm'.
3685 .  o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
3686            submatrix (same value is used for all local rows).
3687 -  o_nnz - array containing the number of nonzeros in the various rows of the
3688            OFF-DIAGONAL portion of the local submatrix (possibly different for
3689            each row) or NULL, if o_nz is used to specify the nonzero
3690            structure. The size of this array is equal to the number
3691            of local rows, i.e 'm'.
3692 
3693    Output Parameter:
3694 .  A - the matrix
3695 
3696    It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions(),
3697    MatXXXXSetPreallocation() paradgm instead of this routine directly.
3698    [MatXXXXSetPreallocation() is, for example, MatSeqAIJSetPreallocation]
3699 
3700    Notes:
3701    If the *_nnz parameter is given then the *_nz parameter is ignored
3702 
3703    m,n,M,N parameters specify the size of the matrix, and its partitioning across
3704    processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
3705    storage requirements for this matrix.
3706 
3707    If PETSC_DECIDE or  PETSC_DETERMINE is used for a particular argument on one
3708    processor than it must be used on all processors that share the object for
3709    that argument.
3710 
3711    The user MUST specify either the local or global matrix dimensions
3712    (possibly both).
3713 
3714    The parallel matrix is partitioned across processors such that the
3715    first m0 rows belong to process 0, the next m1 rows belong to
3716    process 1, the next m2 rows belong to process 2 etc.. where
3717    m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
3718    values corresponding to [m x N] submatrix.
3719 
3720    The columns are logically partitioned with the n0 columns belonging
3721    to 0th partition, the next n1 columns belonging to the next
3722    partition etc.. where n0,n1,n2... are the input parameter 'n'.
3723 
3724    The DIAGONAL portion of the local submatrix on any given processor
3725    is the submatrix corresponding to the rows and columns m,n
3726    corresponding to the given processor. i.e diagonal matrix on
3727    process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
3728    etc. The remaining portion of the local submatrix [m x (N-n)]
3729    constitute the OFF-DIAGONAL portion. The example below better
3730    illustrates this concept.
3731 
3732    For a square global matrix we define each processor's diagonal portion
3733    to be its local rows and the corresponding columns (a square submatrix);
3734    each processor's off-diagonal portion encompasses the remainder of the
3735    local matrix (a rectangular submatrix).
3736 
3737    If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
3738 
3739    When calling this routine with a single process communicator, a matrix of
3740    type SEQAIJ is returned.  If a matrix of type MATMPIAIJ is desired for this
3741    type of communicator, use the construction mechanism:
3742      MatCreate(...,&A); MatSetType(A,MATMPIAIJ); MatSetSizes(A, m,n,M,N); MatMPIAIJSetPreallocation(A,...);
3743 
3744    By default, this format uses inodes (identical nodes) when possible.
3745    We search for consecutive rows with the same nonzero structure, thereby
3746    reusing matrix information to achieve increased efficiency.
3747 
3748    Options Database Keys:
3749 +  -mat_no_inode  - Do not use inodes
3750 .  -mat_inode_limit <limit> - Sets inode limit (max limit=5)
3751 -  -mat_aij_oneindex - Internally use indexing starting at 1
3752         rather than 0.  Note that when calling MatSetValues(),
3753         the user still MUST index entries starting at 0!
3754 
3755 
3756    Example usage:
3757 
3758    Consider the following 8x8 matrix with 34 non-zero values, that is
3759    assembled across 3 processors. Lets assume that proc0 owns 3 rows,
3760    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
3761    as follows:
3762 
3763 .vb
3764             1  2  0  |  0  3  0  |  0  4
3765     Proc0   0  5  6  |  7  0  0  |  8  0
3766             9  0 10  | 11  0  0  | 12  0
3767     -------------------------------------
3768            13  0 14  | 15 16 17  |  0  0
3769     Proc1   0 18  0  | 19 20 21  |  0  0
3770             0  0  0  | 22 23  0  | 24  0
3771     -------------------------------------
3772     Proc2  25 26 27  |  0  0 28  | 29  0
3773            30  0  0  | 31 32 33  |  0 34
3774 .ve
3775 
3776    This can be represented as a collection of submatrices as:
3777 
3778 .vb
3779       A B C
3780       D E F
3781       G H I
3782 .ve
3783 
3784    Where the submatrices A,B,C are owned by proc0, D,E,F are
3785    owned by proc1, G,H,I are owned by proc2.
3786 
3787    The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3788    The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
3789    The 'M','N' parameters are 8,8, and have the same values on all procs.
3790 
3791    The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
3792    submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
3793    corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
3794    Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
3795    part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
3796    matrix, ans [DF] as another SeqAIJ matrix.
3797 
3798    When d_nz, o_nz parameters are specified, d_nz storage elements are
3799    allocated for every row of the local diagonal submatrix, and o_nz
3800    storage locations are allocated for every row of the OFF-DIAGONAL submat.
3801    One way to choose d_nz and o_nz is to use the max nonzerors per local
3802    rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
3803    In this case, the values of d_nz,o_nz are:
3804 .vb
3805      proc0 : dnz = 2, o_nz = 2
3806      proc1 : dnz = 3, o_nz = 2
3807      proc2 : dnz = 1, o_nz = 4
3808 .ve
3809    We are allocating m*(d_nz+o_nz) storage locations for every proc. This
3810    translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
3811    for proc3. i.e we are using 12+15+10=37 storage locations to store
3812    34 values.
3813 
3814    When d_nnz, o_nnz parameters are specified, the storage is specified
3815    for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
3816    In the above case the values for d_nnz,o_nnz are:
3817 .vb
3818      proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
3819      proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
3820      proc2: d_nnz = [1,1]   and o_nnz = [4,4]
3821 .ve
3822    Here the space allocated is sum of all the above values i.e 34, and
3823    hence pre-allocation is perfect.
3824 
3825    Level: intermediate
3826 
3827 .keywords: matrix, aij, compressed row, sparse, parallel
3828 
3829 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
3830           MATMPIAIJ, MatCreateMPIAIJWithArrays()
3831 @*/
3832 PetscErrorCode  MatCreateAIJ(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[],Mat *A)
3833 {
3834   PetscErrorCode ierr;
3835   PetscMPIInt    size;
3836 
3837   PetscFunctionBegin;
3838   ierr = MatCreate(comm,A);CHKERRQ(ierr);
3839   ierr = MatSetSizes(*A,m,n,M,N);CHKERRQ(ierr);
3840   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
3841   if (size > 1) {
3842     ierr = MatSetType(*A,MATMPIAIJ);CHKERRQ(ierr);
3843     ierr = MatMPIAIJSetPreallocation(*A,d_nz,d_nnz,o_nz,o_nnz);CHKERRQ(ierr);
3844   } else {
3845     ierr = MatSetType(*A,MATSEQAIJ);CHKERRQ(ierr);
3846     ierr = MatSeqAIJSetPreallocation(*A,d_nz,d_nnz);CHKERRQ(ierr);
3847   }
3848   PetscFunctionReturn(0);
3849 }
3850 
3851 PetscErrorCode  MatMPIAIJGetSeqAIJ(Mat A,Mat *Ad,Mat *Ao,const PetscInt *colmap[])
3852 {
3853   Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
3854   PetscBool      flg;
3855   PetscErrorCode ierr;
3856 
3857   PetscFunctionBegin;
3858   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);CHKERRQ(ierr);
3859   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"This function requires a MATMPIAIJ matrix as input");
3860   if (Ad)     *Ad     = a->A;
3861   if (Ao)     *Ao     = a->B;
3862   if (colmap) *colmap = a->garray;
3863   PetscFunctionReturn(0);
3864 }
3865 
3866 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm,Mat inmat,PetscInt n,MatReuse scall,Mat *outmat)
3867 {
3868   PetscErrorCode ierr;
3869   PetscInt       m,N,i,rstart,nnz,Ii;
3870   PetscInt       *indx;
3871   PetscScalar    *values;
3872 
3873   PetscFunctionBegin;
3874   ierr = MatGetSize(inmat,&m,&N);CHKERRQ(ierr);
3875   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
3876     PetscInt       *dnz,*onz,sum,bs,cbs;
3877 
3878     if (n == PETSC_DECIDE) {
3879       ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
3880     }
3881     /* Check sum(n) = N */
3882     ierr = MPIU_Allreduce(&n,&sum,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3883     if (sum != N) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Sum of local columns != global columns %d",N);
3884 
3885     ierr    = MPI_Scan(&m, &rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
3886     rstart -= m;
3887 
3888     ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
3889     for (i=0; i<m; i++) {
3890       ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3891       ierr = MatPreallocateSet(i+rstart,nnz,indx,dnz,onz);CHKERRQ(ierr);
3892       ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,NULL);CHKERRQ(ierr);
3893     }
3894 
3895     ierr = MatCreate(comm,outmat);CHKERRQ(ierr);
3896     ierr = MatSetSizes(*outmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
3897     ierr = MatGetBlockSizes(inmat,&bs,&cbs);CHKERRQ(ierr);
3898     ierr = MatSetBlockSizes(*outmat,bs,cbs);CHKERRQ(ierr);
3899     ierr = MatSetType(*outmat,MATAIJ);CHKERRQ(ierr);
3900     ierr = MatSeqAIJSetPreallocation(*outmat,0,dnz);CHKERRQ(ierr);
3901     ierr = MatMPIAIJSetPreallocation(*outmat,0,dnz,0,onz);CHKERRQ(ierr);
3902     ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
3903   }
3904 
3905   /* numeric phase */
3906   ierr = MatGetOwnershipRange(*outmat,&rstart,NULL);CHKERRQ(ierr);
3907   for (i=0; i<m; i++) {
3908     ierr = MatGetRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3909     Ii   = i + rstart;
3910     ierr = MatSetValues(*outmat,1,&Ii,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3911     ierr = MatRestoreRow_SeqAIJ(inmat,i,&nnz,&indx,&values);CHKERRQ(ierr);
3912   }
3913   ierr = MatAssemblyBegin(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3914   ierr = MatAssemblyEnd(*outmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3915   PetscFunctionReturn(0);
3916 }
3917 
3918 PetscErrorCode MatFileSplit(Mat A,char *outfile)
3919 {
3920   PetscErrorCode    ierr;
3921   PetscMPIInt       rank;
3922   PetscInt          m,N,i,rstart,nnz;
3923   size_t            len;
3924   const PetscInt    *indx;
3925   PetscViewer       out;
3926   char              *name;
3927   Mat               B;
3928   const PetscScalar *values;
3929 
3930   PetscFunctionBegin;
3931   ierr = MatGetLocalSize(A,&m,0);CHKERRQ(ierr);
3932   ierr = MatGetSize(A,0,&N);CHKERRQ(ierr);
3933   /* Should this be the type of the diagonal block of A? */
3934   ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
3935   ierr = MatSetSizes(B,m,N,m,N);CHKERRQ(ierr);
3936   ierr = MatSetBlockSizesFromMats(B,A,A);CHKERRQ(ierr);
3937   ierr = MatSetType(B,MATSEQAIJ);CHKERRQ(ierr);
3938   ierr = MatSeqAIJSetPreallocation(B,0,NULL);CHKERRQ(ierr);
3939   ierr = MatGetOwnershipRange(A,&rstart,0);CHKERRQ(ierr);
3940   for (i=0; i<m; i++) {
3941     ierr = MatGetRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3942     ierr = MatSetValues(B,1,&i,nnz,indx,values,INSERT_VALUES);CHKERRQ(ierr);
3943     ierr = MatRestoreRow(A,i+rstart,&nnz,&indx,&values);CHKERRQ(ierr);
3944   }
3945   ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3946   ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
3947 
3948   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A),&rank);CHKERRQ(ierr);
3949   ierr = PetscStrlen(outfile,&len);CHKERRQ(ierr);
3950   ierr = PetscMalloc1(len+5,&name);CHKERRQ(ierr);
3951   sprintf(name,"%s.%d",outfile,rank);
3952   ierr = PetscViewerBinaryOpen(PETSC_COMM_SELF,name,FILE_MODE_APPEND,&out);CHKERRQ(ierr);
3953   ierr = PetscFree(name);CHKERRQ(ierr);
3954   ierr = MatView(B,out);CHKERRQ(ierr);
3955   ierr = PetscViewerDestroy(&out);CHKERRQ(ierr);
3956   ierr = MatDestroy(&B);CHKERRQ(ierr);
3957   PetscFunctionReturn(0);
3958 }
3959 
3960 PetscErrorCode  MatDestroy_MPIAIJ_SeqsToMPI(Mat A)
3961 {
3962   PetscErrorCode      ierr;
3963   Mat_Merge_SeqsToMPI *merge;
3964   PetscContainer      container;
3965 
3966   PetscFunctionBegin;
3967   ierr = PetscObjectQuery((PetscObject)A,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
3968   if (container) {
3969     ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
3970     ierr = PetscFree(merge->id_r);CHKERRQ(ierr);
3971     ierr = PetscFree(merge->len_s);CHKERRQ(ierr);
3972     ierr = PetscFree(merge->len_r);CHKERRQ(ierr);
3973     ierr = PetscFree(merge->bi);CHKERRQ(ierr);
3974     ierr = PetscFree(merge->bj);CHKERRQ(ierr);
3975     ierr = PetscFree(merge->buf_ri[0]);CHKERRQ(ierr);
3976     ierr = PetscFree(merge->buf_ri);CHKERRQ(ierr);
3977     ierr = PetscFree(merge->buf_rj[0]);CHKERRQ(ierr);
3978     ierr = PetscFree(merge->buf_rj);CHKERRQ(ierr);
3979     ierr = PetscFree(merge->coi);CHKERRQ(ierr);
3980     ierr = PetscFree(merge->coj);CHKERRQ(ierr);
3981     ierr = PetscFree(merge->owners_co);CHKERRQ(ierr);
3982     ierr = PetscLayoutDestroy(&merge->rowmap);CHKERRQ(ierr);
3983     ierr = PetscFree(merge);CHKERRQ(ierr);
3984     ierr = PetscObjectCompose((PetscObject)A,"MatMergeSeqsToMPI",0);CHKERRQ(ierr);
3985   }
3986   ierr = MatDestroy_MPIAIJ(A);CHKERRQ(ierr);
3987   PetscFunctionReturn(0);
3988 }
3989 
3990 #include <../src/mat/utils/freespace.h>
3991 #include <petscbt.h>
3992 
3993 PetscErrorCode  MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat,Mat mpimat)
3994 {
3995   PetscErrorCode      ierr;
3996   MPI_Comm            comm;
3997   Mat_SeqAIJ          *a  =(Mat_SeqAIJ*)seqmat->data;
3998   PetscMPIInt         size,rank,taga,*len_s;
3999   PetscInt            N=mpimat->cmap->N,i,j,*owners,*ai=a->i,*aj;
4000   PetscInt            proc,m;
4001   PetscInt            **buf_ri,**buf_rj;
4002   PetscInt            k,anzi,*bj_i,*bi,*bj,arow,bnzi,nextaj;
4003   PetscInt            nrows,**buf_ri_k,**nextrow,**nextai;
4004   MPI_Request         *s_waits,*r_waits;
4005   MPI_Status          *status;
4006   MatScalar           *aa=a->a;
4007   MatScalar           **abuf_r,*ba_i;
4008   Mat_Merge_SeqsToMPI *merge;
4009   PetscContainer      container;
4010 
4011   PetscFunctionBegin;
4012   ierr = PetscObjectGetComm((PetscObject)mpimat,&comm);CHKERRQ(ierr);
4013   ierr = PetscLogEventBegin(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4014 
4015   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4016   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4017 
4018   ierr = PetscObjectQuery((PetscObject)mpimat,"MatMergeSeqsToMPI",(PetscObject*)&container);CHKERRQ(ierr);
4019   ierr = PetscContainerGetPointer(container,(void**)&merge);CHKERRQ(ierr);
4020 
4021   bi     = merge->bi;
4022   bj     = merge->bj;
4023   buf_ri = merge->buf_ri;
4024   buf_rj = merge->buf_rj;
4025 
4026   ierr   = PetscMalloc1(size,&status);CHKERRQ(ierr);
4027   owners = merge->rowmap->range;
4028   len_s  = merge->len_s;
4029 
4030   /* send and recv matrix values */
4031   /*-----------------------------*/
4032   ierr = PetscObjectGetNewTag((PetscObject)mpimat,&taga);CHKERRQ(ierr);
4033   ierr = PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);CHKERRQ(ierr);
4034 
4035   ierr = PetscMalloc1(merge->nsend+1,&s_waits);CHKERRQ(ierr);
4036   for (proc=0,k=0; proc<size; proc++) {
4037     if (!len_s[proc]) continue;
4038     i    = owners[proc];
4039     ierr = MPI_Isend(aa+ai[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);CHKERRQ(ierr);
4040     k++;
4041   }
4042 
4043   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,r_waits,status);CHKERRQ(ierr);}
4044   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,s_waits,status);CHKERRQ(ierr);}
4045   ierr = PetscFree(status);CHKERRQ(ierr);
4046 
4047   ierr = PetscFree(s_waits);CHKERRQ(ierr);
4048   ierr = PetscFree(r_waits);CHKERRQ(ierr);
4049 
4050   /* insert mat values of mpimat */
4051   /*----------------------------*/
4052   ierr = PetscMalloc1(N,&ba_i);CHKERRQ(ierr);
4053   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4054 
4055   for (k=0; k<merge->nrecv; k++) {
4056     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4057     nrows       = *(buf_ri_k[k]);
4058     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
4059     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4060   }
4061 
4062   /* set values of ba */
4063   m = merge->rowmap->n;
4064   for (i=0; i<m; i++) {
4065     arow = owners[rank] + i;
4066     bj_i = bj+bi[i];  /* col indices of the i-th row of mpimat */
4067     bnzi = bi[i+1] - bi[i];
4068     ierr = PetscMemzero(ba_i,bnzi*sizeof(PetscScalar));CHKERRQ(ierr);
4069 
4070     /* add local non-zero vals of this proc's seqmat into ba */
4071     anzi   = ai[arow+1] - ai[arow];
4072     aj     = a->j + ai[arow];
4073     aa     = a->a + ai[arow];
4074     nextaj = 0;
4075     for (j=0; nextaj<anzi; j++) {
4076       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4077         ba_i[j] += aa[nextaj++];
4078       }
4079     }
4080 
4081     /* add received vals into ba */
4082     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4083       /* i-th row */
4084       if (i == *nextrow[k]) {
4085         anzi   = *(nextai[k]+1) - *nextai[k];
4086         aj     = buf_rj[k] + *(nextai[k]);
4087         aa     = abuf_r[k] + *(nextai[k]);
4088         nextaj = 0;
4089         for (j=0; nextaj<anzi; j++) {
4090           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4091             ba_i[j] += aa[nextaj++];
4092           }
4093         }
4094         nextrow[k]++; nextai[k]++;
4095       }
4096     }
4097     ierr = MatSetValues(mpimat,1,&arow,bnzi,bj_i,ba_i,INSERT_VALUES);CHKERRQ(ierr);
4098   }
4099   ierr = MatAssemblyBegin(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4100   ierr = MatAssemblyEnd(mpimat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4101 
4102   ierr = PetscFree(abuf_r[0]);CHKERRQ(ierr);
4103   ierr = PetscFree(abuf_r);CHKERRQ(ierr);
4104   ierr = PetscFree(ba_i);CHKERRQ(ierr);
4105   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4106   ierr = PetscLogEventEnd(MAT_Seqstompinum,seqmat,0,0,0);CHKERRQ(ierr);
4107   PetscFunctionReturn(0);
4108 }
4109 
4110 PetscErrorCode  MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,Mat *mpimat)
4111 {
4112   PetscErrorCode      ierr;
4113   Mat                 B_mpi;
4114   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)seqmat->data;
4115   PetscMPIInt         size,rank,tagi,tagj,*len_s,*len_si,*len_ri;
4116   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
4117   PetscInt            M=seqmat->rmap->n,N=seqmat->cmap->n,i,*owners,*ai=a->i,*aj=a->j;
4118   PetscInt            len,proc,*dnz,*onz,bs,cbs;
4119   PetscInt            k,anzi,*bi,*bj,*lnk,nlnk,arow,bnzi,nspacedouble=0;
4120   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextai;
4121   MPI_Request         *si_waits,*sj_waits,*ri_waits,*rj_waits;
4122   MPI_Status          *status;
4123   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
4124   PetscBT             lnkbt;
4125   Mat_Merge_SeqsToMPI *merge;
4126   PetscContainer      container;
4127 
4128   PetscFunctionBegin;
4129   ierr = PetscLogEventBegin(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4130 
4131   /* make sure it is a PETSc comm */
4132   ierr = PetscCommDuplicate(comm,&comm,NULL);CHKERRQ(ierr);
4133   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4134   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4135 
4136   ierr = PetscNew(&merge);CHKERRQ(ierr);
4137   ierr = PetscMalloc1(size,&status);CHKERRQ(ierr);
4138 
4139   /* determine row ownership */
4140   /*---------------------------------------------------------*/
4141   ierr = PetscLayoutCreate(comm,&merge->rowmap);CHKERRQ(ierr);
4142   ierr = PetscLayoutSetLocalSize(merge->rowmap,m);CHKERRQ(ierr);
4143   ierr = PetscLayoutSetSize(merge->rowmap,M);CHKERRQ(ierr);
4144   ierr = PetscLayoutSetBlockSize(merge->rowmap,1);CHKERRQ(ierr);
4145   ierr = PetscLayoutSetUp(merge->rowmap);CHKERRQ(ierr);
4146   ierr = PetscMalloc1(size,&len_si);CHKERRQ(ierr);
4147   ierr = PetscMalloc1(size,&merge->len_s);CHKERRQ(ierr);
4148 
4149   m      = merge->rowmap->n;
4150   owners = merge->rowmap->range;
4151 
4152   /* determine the number of messages to send, their lengths */
4153   /*---------------------------------------------------------*/
4154   len_s = merge->len_s;
4155 
4156   len          = 0; /* length of buf_si[] */
4157   merge->nsend = 0;
4158   for (proc=0; proc<size; proc++) {
4159     len_si[proc] = 0;
4160     if (proc == rank) {
4161       len_s[proc] = 0;
4162     } else {
4163       len_si[proc] = owners[proc+1] - owners[proc] + 1;
4164       len_s[proc]  = ai[owners[proc+1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4165     }
4166     if (len_s[proc]) {
4167       merge->nsend++;
4168       nrows = 0;
4169       for (i=owners[proc]; i<owners[proc+1]; i++) {
4170         if (ai[i+1] > ai[i]) nrows++;
4171       }
4172       len_si[proc] = 2*(nrows+1);
4173       len         += len_si[proc];
4174     }
4175   }
4176 
4177   /* determine the number and length of messages to receive for ij-structure */
4178   /*-------------------------------------------------------------------------*/
4179   ierr = PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);CHKERRQ(ierr);
4180   ierr = PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);CHKERRQ(ierr);
4181 
4182   /* post the Irecv of j-structure */
4183   /*-------------------------------*/
4184   ierr = PetscCommGetNewTag(comm,&tagj);CHKERRQ(ierr);
4185   ierr = PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rj_waits);CHKERRQ(ierr);
4186 
4187   /* post the Isend of j-structure */
4188   /*--------------------------------*/
4189   ierr = PetscMalloc2(merge->nsend,&si_waits,merge->nsend,&sj_waits);CHKERRQ(ierr);
4190 
4191   for (proc=0, k=0; proc<size; proc++) {
4192     if (!len_s[proc]) continue;
4193     i    = owners[proc];
4194     ierr = MPI_Isend(aj+ai[i],len_s[proc],MPIU_INT,proc,tagj,comm,sj_waits+k);CHKERRQ(ierr);
4195     k++;
4196   }
4197 
4198   /* receives and sends of j-structure are complete */
4199   /*------------------------------------------------*/
4200   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,rj_waits,status);CHKERRQ(ierr);}
4201   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,sj_waits,status);CHKERRQ(ierr);}
4202 
4203   /* send and recv i-structure */
4204   /*---------------------------*/
4205   ierr = PetscCommGetNewTag(comm,&tagi);CHKERRQ(ierr);
4206   ierr = PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&ri_waits);CHKERRQ(ierr);
4207 
4208   ierr   = PetscMalloc1(len+1,&buf_s);CHKERRQ(ierr);
4209   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
4210   for (proc=0,k=0; proc<size; proc++) {
4211     if (!len_s[proc]) continue;
4212     /* form outgoing message for i-structure:
4213          buf_si[0]:                 nrows to be sent
4214                [1:nrows]:           row index (global)
4215                [nrows+1:2*nrows+1]: i-structure index
4216     */
4217     /*-------------------------------------------*/
4218     nrows       = len_si[proc]/2 - 1;
4219     buf_si_i    = buf_si + nrows+1;
4220     buf_si[0]   = nrows;
4221     buf_si_i[0] = 0;
4222     nrows       = 0;
4223     for (i=owners[proc]; i<owners[proc+1]; i++) {
4224       anzi = ai[i+1] - ai[i];
4225       if (anzi) {
4226         buf_si_i[nrows+1] = buf_si_i[nrows] + anzi; /* i-structure */
4227         buf_si[nrows+1]   = i-owners[proc]; /* local row index */
4228         nrows++;
4229       }
4230     }
4231     ierr = MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,si_waits+k);CHKERRQ(ierr);
4232     k++;
4233     buf_si += len_si[proc];
4234   }
4235 
4236   if (merge->nrecv) {ierr = MPI_Waitall(merge->nrecv,ri_waits,status);CHKERRQ(ierr);}
4237   if (merge->nsend) {ierr = MPI_Waitall(merge->nsend,si_waits,status);CHKERRQ(ierr);}
4238 
4239   ierr = PetscInfo2(seqmat,"nsend: %D, nrecv: %D\n",merge->nsend,merge->nrecv);CHKERRQ(ierr);
4240   for (i=0; i<merge->nrecv; i++) {
4241     ierr = PetscInfo3(seqmat,"recv len_ri=%D, len_rj=%D from [%D]\n",len_ri[i],merge->len_r[i],merge->id_r[i]);CHKERRQ(ierr);
4242   }
4243 
4244   ierr = PetscFree(len_si);CHKERRQ(ierr);
4245   ierr = PetscFree(len_ri);CHKERRQ(ierr);
4246   ierr = PetscFree(rj_waits);CHKERRQ(ierr);
4247   ierr = PetscFree2(si_waits,sj_waits);CHKERRQ(ierr);
4248   ierr = PetscFree(ri_waits);CHKERRQ(ierr);
4249   ierr = PetscFree(buf_s);CHKERRQ(ierr);
4250   ierr = PetscFree(status);CHKERRQ(ierr);
4251 
4252   /* compute a local seq matrix in each processor */
4253   /*----------------------------------------------*/
4254   /* allocate bi array and free space for accumulating nonzero column info */
4255   ierr  = PetscMalloc1(m+1,&bi);CHKERRQ(ierr);
4256   bi[0] = 0;
4257 
4258   /* create and initialize a linked list */
4259   nlnk = N+1;
4260   ierr = PetscLLCreate(N,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4261 
4262   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4263   len  = ai[owners[rank+1]] - ai[owners[rank]];
4264   ierr = PetscFreeSpaceGet(PetscIntMultTruncate(2,len)+1,&free_space);CHKERRQ(ierr);
4265 
4266   current_space = free_space;
4267 
4268   /* determine symbolic info for each local row */
4269   ierr = PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextai);CHKERRQ(ierr);
4270 
4271   for (k=0; k<merge->nrecv; k++) {
4272     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4273     nrows       = *buf_ri_k[k];
4274     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
4275     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
4276   }
4277 
4278   ierr = MatPreallocateInitialize(comm,m,n,dnz,onz);CHKERRQ(ierr);
4279   len  = 0;
4280   for (i=0; i<m; i++) {
4281     bnzi = 0;
4282     /* add local non-zero cols of this proc's seqmat into lnk */
4283     arow  = owners[rank] + i;
4284     anzi  = ai[arow+1] - ai[arow];
4285     aj    = a->j + ai[arow];
4286     ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4287     bnzi += nlnk;
4288     /* add received col data into lnk */
4289     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
4290       if (i == *nextrow[k]) { /* i-th row */
4291         anzi  = *(nextai[k]+1) - *nextai[k];
4292         aj    = buf_rj[k] + *nextai[k];
4293         ierr  = PetscLLAddSorted(anzi,aj,N,nlnk,lnk,lnkbt);CHKERRQ(ierr);
4294         bnzi += nlnk;
4295         nextrow[k]++; nextai[k]++;
4296       }
4297     }
4298     if (len < bnzi) len = bnzi;  /* =max(bnzi) */
4299 
4300     /* if free space is not available, make more free space */
4301     if (current_space->local_remaining<bnzi) {
4302       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(bnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
4303       nspacedouble++;
4304     }
4305     /* copy data into free space, then initialize lnk */
4306     ierr = PetscLLClean(N,N,bnzi,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
4307     ierr = MatPreallocateSet(i+owners[rank],bnzi,current_space->array,dnz,onz);CHKERRQ(ierr);
4308 
4309     current_space->array           += bnzi;
4310     current_space->local_used      += bnzi;
4311     current_space->local_remaining -= bnzi;
4312 
4313     bi[i+1] = bi[i] + bnzi;
4314   }
4315 
4316   ierr = PetscFree3(buf_ri_k,nextrow,nextai);CHKERRQ(ierr);
4317 
4318   ierr = PetscMalloc1(bi[m]+1,&bj);CHKERRQ(ierr);
4319   ierr = PetscFreeSpaceContiguous(&free_space,bj);CHKERRQ(ierr);
4320   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4321 
4322   /* create symbolic parallel matrix B_mpi */
4323   /*---------------------------------------*/
4324   ierr = MatGetBlockSizes(seqmat,&bs,&cbs);CHKERRQ(ierr);
4325   ierr = MatCreate(comm,&B_mpi);CHKERRQ(ierr);
4326   if (n==PETSC_DECIDE) {
4327     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,N);CHKERRQ(ierr);
4328   } else {
4329     ierr = MatSetSizes(B_mpi,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4330   }
4331   ierr = MatSetBlockSizes(B_mpi,bs,cbs);CHKERRQ(ierr);
4332   ierr = MatSetType(B_mpi,MATMPIAIJ);CHKERRQ(ierr);
4333   ierr = MatMPIAIJSetPreallocation(B_mpi,0,dnz,0,onz);CHKERRQ(ierr);
4334   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
4335   ierr = MatSetOption(B_mpi,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
4336 
4337   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
4338   B_mpi->assembled    = PETSC_FALSE;
4339   B_mpi->ops->destroy = MatDestroy_MPIAIJ_SeqsToMPI;
4340   merge->bi           = bi;
4341   merge->bj           = bj;
4342   merge->buf_ri       = buf_ri;
4343   merge->buf_rj       = buf_rj;
4344   merge->coi          = NULL;
4345   merge->coj          = NULL;
4346   merge->owners_co    = NULL;
4347 
4348   ierr = PetscCommDestroy(&comm);CHKERRQ(ierr);
4349 
4350   /* attach the supporting struct to B_mpi for reuse */
4351   ierr    = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
4352   ierr    = PetscContainerSetPointer(container,merge);CHKERRQ(ierr);
4353   ierr    = PetscObjectCompose((PetscObject)B_mpi,"MatMergeSeqsToMPI",(PetscObject)container);CHKERRQ(ierr);
4354   ierr    = PetscContainerDestroy(&container);CHKERRQ(ierr);
4355   *mpimat = B_mpi;
4356 
4357   ierr = PetscLogEventEnd(MAT_Seqstompisym,seqmat,0,0,0);CHKERRQ(ierr);
4358   PetscFunctionReturn(0);
4359 }
4360 
4361 /*@C
4362       MatCreateMPIAIJSumSeqAIJ - Creates a MATMPIAIJ matrix by adding sequential
4363                  matrices from each processor
4364 
4365     Collective on MPI_Comm
4366 
4367    Input Parameters:
4368 +    comm - the communicators the parallel matrix will live on
4369 .    seqmat - the input sequential matrices
4370 .    m - number of local rows (or PETSC_DECIDE)
4371 .    n - number of local columns (or PETSC_DECIDE)
4372 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4373 
4374    Output Parameter:
4375 .    mpimat - the parallel matrix generated
4376 
4377     Level: advanced
4378 
4379    Notes:
4380      The dimensions of the sequential matrix in each processor MUST be the same.
4381      The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
4382      destroyed when mpimat is destroyed. Call PetscObjectQuery() to access seqmat.
4383 @*/
4384 PetscErrorCode  MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm,Mat seqmat,PetscInt m,PetscInt n,MatReuse scall,Mat *mpimat)
4385 {
4386   PetscErrorCode ierr;
4387   PetscMPIInt    size;
4388 
4389   PetscFunctionBegin;
4390   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4391   if (size == 1) {
4392     ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4393     if (scall == MAT_INITIAL_MATRIX) {
4394       ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
4395     } else {
4396       ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
4397     }
4398     ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4399     PetscFunctionReturn(0);
4400   }
4401   ierr = PetscLogEventBegin(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4402   if (scall == MAT_INITIAL_MATRIX) {
4403     ierr = MatCreateMPIAIJSumSeqAIJSymbolic(comm,seqmat,m,n,mpimat);CHKERRQ(ierr);
4404   }
4405   ierr = MatCreateMPIAIJSumSeqAIJNumeric(seqmat,*mpimat);CHKERRQ(ierr);
4406   ierr = PetscLogEventEnd(MAT_Seqstompi,seqmat,0,0,0);CHKERRQ(ierr);
4407   PetscFunctionReturn(0);
4408 }
4409 
4410 /*@
4411      MatMPIAIJGetLocalMat - Creates a SeqAIJ from a MATMPIAIJ matrix by taking all its local rows and putting them into a sequential vector with
4412           mlocal rows and n columns. Where mlocal is the row count obtained with MatGetLocalSize() and n is the global column count obtained
4413           with MatGetSize()
4414 
4415     Not Collective
4416 
4417    Input Parameters:
4418 +    A - the matrix
4419 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4420 
4421    Output Parameter:
4422 .    A_loc - the local sequential matrix generated
4423 
4424     Level: developer
4425 
4426 .seealso: MatGetOwnerShipRange(), MatMPIAIJGetLocalMatCondensed()
4427 
4428 @*/
4429 PetscErrorCode  MatMPIAIJGetLocalMat(Mat A,MatReuse scall,Mat *A_loc)
4430 {
4431   PetscErrorCode ierr;
4432   Mat_MPIAIJ     *mpimat=(Mat_MPIAIJ*)A->data;
4433   Mat_SeqAIJ     *mat,*a,*b;
4434   PetscInt       *ai,*aj,*bi,*bj,*cmap=mpimat->garray;
4435   MatScalar      *aa,*ba,*cam;
4436   PetscScalar    *ca;
4437   PetscInt       am=A->rmap->n,i,j,k,cstart=A->cmap->rstart;
4438   PetscInt       *ci,*cj,col,ncols_d,ncols_o,jo;
4439   PetscBool      match;
4440   MPI_Comm       comm;
4441   PetscMPIInt    size;
4442 
4443   PetscFunctionBegin;
4444   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4445   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4446   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4447   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4448   if (size == 1 && scall == MAT_REUSE_MATRIX) PetscFunctionReturn(0);
4449 
4450   ierr = PetscLogEventBegin(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4451   a = (Mat_SeqAIJ*)(mpimat->A)->data;
4452   b = (Mat_SeqAIJ*)(mpimat->B)->data;
4453   ai = a->i; aj = a->j; bi = b->i; bj = b->j;
4454   aa = a->a; ba = b->a;
4455   if (scall == MAT_INITIAL_MATRIX) {
4456     if (size == 1) {
4457       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ai,aj,aa,A_loc);CHKERRQ(ierr);
4458       PetscFunctionReturn(0);
4459     }
4460 
4461     ierr  = PetscMalloc1(1+am,&ci);CHKERRQ(ierr);
4462     ci[0] = 0;
4463     for (i=0; i<am; i++) {
4464       ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
4465     }
4466     ierr = PetscMalloc1(1+ci[am],&cj);CHKERRQ(ierr);
4467     ierr = PetscMalloc1(1+ci[am],&ca);CHKERRQ(ierr);
4468     k    = 0;
4469     for (i=0; i<am; i++) {
4470       ncols_o = bi[i+1] - bi[i];
4471       ncols_d = ai[i+1] - ai[i];
4472       /* off-diagonal portion of A */
4473       for (jo=0; jo<ncols_o; jo++) {
4474         col = cmap[*bj];
4475         if (col >= cstart) break;
4476         cj[k]   = col; bj++;
4477         ca[k++] = *ba++;
4478       }
4479       /* diagonal portion of A */
4480       for (j=0; j<ncols_d; j++) {
4481         cj[k]   = cstart + *aj++;
4482         ca[k++] = *aa++;
4483       }
4484       /* off-diagonal portion of A */
4485       for (j=jo; j<ncols_o; j++) {
4486         cj[k]   = cmap[*bj++];
4487         ca[k++] = *ba++;
4488       }
4489     }
4490     /* put together the new matrix */
4491     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,A->cmap->N,ci,cj,ca,A_loc);CHKERRQ(ierr);
4492     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4493     /* Since these are PETSc arrays, change flags to free them as necessary. */
4494     mat          = (Mat_SeqAIJ*)(*A_loc)->data;
4495     mat->free_a  = PETSC_TRUE;
4496     mat->free_ij = PETSC_TRUE;
4497     mat->nonew   = 0;
4498   } else if (scall == MAT_REUSE_MATRIX) {
4499     mat=(Mat_SeqAIJ*)(*A_loc)->data;
4500     ci = mat->i; cj = mat->j; cam = mat->a;
4501     for (i=0; i<am; i++) {
4502       /* off-diagonal portion of A */
4503       ncols_o = bi[i+1] - bi[i];
4504       for (jo=0; jo<ncols_o; jo++) {
4505         col = cmap[*bj];
4506         if (col >= cstart) break;
4507         *cam++ = *ba++; bj++;
4508       }
4509       /* diagonal portion of A */
4510       ncols_d = ai[i+1] - ai[i];
4511       for (j=0; j<ncols_d; j++) *cam++ = *aa++;
4512       /* off-diagonal portion of A */
4513       for (j=jo; j<ncols_o; j++) {
4514         *cam++ = *ba++; bj++;
4515       }
4516     }
4517   } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
4518   ierr = PetscLogEventEnd(MAT_Getlocalmat,A,0,0,0);CHKERRQ(ierr);
4519   PetscFunctionReturn(0);
4520 }
4521 
4522 /*@C
4523      MatMPIAIJGetLocalMatCondensed - Creates a SeqAIJ matrix from an MATMPIAIJ matrix by taking all its local rows and NON-ZERO columns
4524 
4525     Not Collective
4526 
4527    Input Parameters:
4528 +    A - the matrix
4529 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4530 -    row, col - index sets of rows and columns to extract (or NULL)
4531 
4532    Output Parameter:
4533 .    A_loc - the local sequential matrix generated
4534 
4535     Level: developer
4536 
4537 .seealso: MatGetOwnershipRange(), MatMPIAIJGetLocalMat()
4538 
4539 @*/
4540 PetscErrorCode  MatMPIAIJGetLocalMatCondensed(Mat A,MatReuse scall,IS *row,IS *col,Mat *A_loc)
4541 {
4542   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4543   PetscErrorCode ierr;
4544   PetscInt       i,start,end,ncols,nzA,nzB,*cmap,imark,*idx;
4545   IS             isrowa,iscola;
4546   Mat            *aloc;
4547   PetscBool      match;
4548 
4549   PetscFunctionBegin;
4550   ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&match);CHKERRQ(ierr);
4551   if (!match) SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP,"Requires MATMPIAIJ matrix as input");
4552   ierr = PetscLogEventBegin(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4553   if (!row) {
4554     start = A->rmap->rstart; end = A->rmap->rend;
4555     ierr  = ISCreateStride(PETSC_COMM_SELF,end-start,start,1,&isrowa);CHKERRQ(ierr);
4556   } else {
4557     isrowa = *row;
4558   }
4559   if (!col) {
4560     start = A->cmap->rstart;
4561     cmap  = a->garray;
4562     nzA   = a->A->cmap->n;
4563     nzB   = a->B->cmap->n;
4564     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4565     ncols = 0;
4566     for (i=0; i<nzB; i++) {
4567       if (cmap[i] < start) idx[ncols++] = cmap[i];
4568       else break;
4569     }
4570     imark = i;
4571     for (i=0; i<nzA; i++) idx[ncols++] = start + i;
4572     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i];
4573     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&iscola);CHKERRQ(ierr);
4574   } else {
4575     iscola = *col;
4576   }
4577   if (scall != MAT_INITIAL_MATRIX) {
4578     ierr    = PetscMalloc1(1,&aloc);CHKERRQ(ierr);
4579     aloc[0] = *A_loc;
4580   }
4581   ierr   = MatCreateSubMatrices(A,1,&isrowa,&iscola,scall,&aloc);CHKERRQ(ierr);
4582   *A_loc = aloc[0];
4583   ierr   = PetscFree(aloc);CHKERRQ(ierr);
4584   if (!row) {
4585     ierr = ISDestroy(&isrowa);CHKERRQ(ierr);
4586   }
4587   if (!col) {
4588     ierr = ISDestroy(&iscola);CHKERRQ(ierr);
4589   }
4590   ierr = PetscLogEventEnd(MAT_Getlocalmatcondensed,A,0,0,0);CHKERRQ(ierr);
4591   PetscFunctionReturn(0);
4592 }
4593 
4594 /*@C
4595     MatGetBrowsOfAcols - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
4596 
4597     Collective on Mat
4598 
4599    Input Parameters:
4600 +    A,B - the matrices in mpiaij format
4601 .    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4602 -    rowb, colb - index sets of rows and columns of B to extract (or NULL)
4603 
4604    Output Parameter:
4605 +    rowb, colb - index sets of rows and columns of B to extract
4606 -    B_seq - the sequential matrix generated
4607 
4608     Level: developer
4609 
4610 @*/
4611 PetscErrorCode  MatGetBrowsOfAcols(Mat A,Mat B,MatReuse scall,IS *rowb,IS *colb,Mat *B_seq)
4612 {
4613   Mat_MPIAIJ     *a=(Mat_MPIAIJ*)A->data;
4614   PetscErrorCode ierr;
4615   PetscInt       *idx,i,start,ncols,nzA,nzB,*cmap,imark;
4616   IS             isrowb,iscolb;
4617   Mat            *bseq=NULL;
4618 
4619   PetscFunctionBegin;
4620   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4621     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
4622   }
4623   ierr = PetscLogEventBegin(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4624 
4625   if (scall == MAT_INITIAL_MATRIX) {
4626     start = A->cmap->rstart;
4627     cmap  = a->garray;
4628     nzA   = a->A->cmap->n;
4629     nzB   = a->B->cmap->n;
4630     ierr  = PetscMalloc1(nzA+nzB, &idx);CHKERRQ(ierr);
4631     ncols = 0;
4632     for (i=0; i<nzB; i++) {  /* row < local row index */
4633       if (cmap[i] < start) idx[ncols++] = cmap[i];
4634       else break;
4635     }
4636     imark = i;
4637     for (i=0; i<nzA; i++) idx[ncols++] = start + i;  /* local rows */
4638     for (i=imark; i<nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
4639     ierr = ISCreateGeneral(PETSC_COMM_SELF,ncols,idx,PETSC_OWN_POINTER,&isrowb);CHKERRQ(ierr);
4640     ierr = ISCreateStride(PETSC_COMM_SELF,B->cmap->N,0,1,&iscolb);CHKERRQ(ierr);
4641   } else {
4642     if (!rowb || !colb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"IS rowb and colb must be provided for MAT_REUSE_MATRIX");
4643     isrowb  = *rowb; iscolb = *colb;
4644     ierr    = PetscMalloc1(1,&bseq);CHKERRQ(ierr);
4645     bseq[0] = *B_seq;
4646   }
4647   ierr   = MatCreateSubMatrices(B,1,&isrowb,&iscolb,scall,&bseq);CHKERRQ(ierr);
4648   *B_seq = bseq[0];
4649   ierr   = PetscFree(bseq);CHKERRQ(ierr);
4650   if (!rowb) {
4651     ierr = ISDestroy(&isrowb);CHKERRQ(ierr);
4652   } else {
4653     *rowb = isrowb;
4654   }
4655   if (!colb) {
4656     ierr = ISDestroy(&iscolb);CHKERRQ(ierr);
4657   } else {
4658     *colb = iscolb;
4659   }
4660   ierr = PetscLogEventEnd(MAT_GetBrowsOfAcols,A,B,0,0);CHKERRQ(ierr);
4661   PetscFunctionReturn(0);
4662 }
4663 
4664 /*
4665     MatGetBrowsOfAoCols_MPIAIJ - Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns
4666     of the OFF-DIAGONAL portion of local A
4667 
4668     Collective on Mat
4669 
4670    Input Parameters:
4671 +    A,B - the matrices in mpiaij format
4672 -    scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
4673 
4674    Output Parameter:
4675 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
4676 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
4677 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
4678 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
4679 
4680     Level: developer
4681 
4682 */
4683 PetscErrorCode  MatGetBrowsOfAoCols_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscInt **startsj_s,PetscInt **startsj_r,MatScalar **bufa_ptr,Mat *B_oth)
4684 {
4685   VecScatter_MPI_General *gen_to,*gen_from;
4686   PetscErrorCode         ierr;
4687   Mat_MPIAIJ             *a=(Mat_MPIAIJ*)A->data;
4688   Mat_SeqAIJ             *b_oth;
4689   VecScatter             ctx =a->Mvctx;
4690   MPI_Comm               comm;
4691   PetscMPIInt            *rprocs,*sprocs,tag=((PetscObject)ctx)->tag,rank;
4692   PetscInt               *rowlen,*bufj,*bufJ,ncols,aBn=a->B->cmap->n,row,*b_othi,*b_othj;
4693   PetscInt               *rvalues,*svalues;
4694   MatScalar              *b_otha,*bufa,*bufA;
4695   PetscInt               i,j,k,l,ll,nrecvs,nsends,nrows,*srow,*rstarts,*rstartsj = 0,*sstarts,*sstartsj,len;
4696   MPI_Request            *rwaits = NULL,*swaits = NULL;
4697   MPI_Status             *sstatus,rstatus;
4698   PetscMPIInt            jj,size;
4699   PetscInt               *cols,sbs,rbs;
4700   PetscScalar            *vals;
4701 
4702   PetscFunctionBegin;
4703   ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
4704   ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
4705 
4706   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) {
4707     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%d, %d) != (%d,%d)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);
4708   }
4709   ierr = PetscLogEventBegin(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4710   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
4711 
4712   if (size == 1) {
4713     startsj_s = NULL;
4714     bufa_ptr  = NULL;
4715     *B_oth    = NULL;
4716     PetscFunctionReturn(0);
4717   }
4718 
4719   gen_to   = (VecScatter_MPI_General*)ctx->todata;
4720   gen_from = (VecScatter_MPI_General*)ctx->fromdata;
4721   nrecvs   = gen_from->n;
4722   nsends   = gen_to->n;
4723 
4724   ierr    = PetscMalloc2(nrecvs,&rwaits,nsends,&swaits);CHKERRQ(ierr);
4725   srow    = gen_to->indices;    /* local row index to be sent */
4726   sstarts = gen_to->starts;
4727   sprocs  = gen_to->procs;
4728   sstatus = gen_to->sstatus;
4729   sbs     = gen_to->bs;
4730   rstarts = gen_from->starts;
4731   rprocs  = gen_from->procs;
4732   rbs     = gen_from->bs;
4733 
4734   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
4735   if (scall == MAT_INITIAL_MATRIX) {
4736     /* i-array */
4737     /*---------*/
4738     /*  post receives */
4739     ierr = PetscMalloc1(rbs*(rstarts[nrecvs] - rstarts[0]),&rvalues);CHKERRQ(ierr);
4740     for (i=0; i<nrecvs; i++) {
4741       rowlen = rvalues + rstarts[i]*rbs;
4742       nrows  = (rstarts[i+1]-rstarts[i])*rbs; /* num of indices to be received */
4743       ierr   = MPI_Irecv(rowlen,nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4744     }
4745 
4746     /* pack the outgoing message */
4747     ierr = PetscMalloc2(nsends+1,&sstartsj,nrecvs+1,&rstartsj);CHKERRQ(ierr);
4748 
4749     sstartsj[0] = 0;
4750     rstartsj[0] = 0;
4751     len         = 0; /* total length of j or a array to be sent */
4752     k           = 0;
4753     ierr = PetscMalloc1(sbs*(sstarts[nsends] - sstarts[0]),&svalues);CHKERRQ(ierr);
4754     for (i=0; i<nsends; i++) {
4755       rowlen = svalues + sstarts[i]*sbs;
4756       nrows  = sstarts[i+1]-sstarts[i]; /* num of block rows */
4757       for (j=0; j<nrows; j++) {
4758         row = srow[k] + B->rmap->range[rank]; /* global row idx */
4759         for (l=0; l<sbs; l++) {
4760           ierr = MatGetRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr); /* rowlength */
4761 
4762           rowlen[j*sbs+l] = ncols;
4763 
4764           len += ncols;
4765           ierr = MatRestoreRow_MPIAIJ(B,row+l,&ncols,NULL,NULL);CHKERRQ(ierr);
4766         }
4767         k++;
4768       }
4769       ierr = MPI_Isend(rowlen,nrows*sbs,MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4770 
4771       sstartsj[i+1] = len;  /* starting point of (i+1)-th outgoing msg in bufj and bufa */
4772     }
4773     /* recvs and sends of i-array are completed */
4774     i = nrecvs;
4775     while (i--) {
4776       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4777     }
4778     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4779     ierr = PetscFree(svalues);CHKERRQ(ierr);
4780 
4781     /* allocate buffers for sending j and a arrays */
4782     ierr = PetscMalloc1(len+1,&bufj);CHKERRQ(ierr);
4783     ierr = PetscMalloc1(len+1,&bufa);CHKERRQ(ierr);
4784 
4785     /* create i-array of B_oth */
4786     ierr = PetscMalloc1(aBn+2,&b_othi);CHKERRQ(ierr);
4787 
4788     b_othi[0] = 0;
4789     len       = 0; /* total length of j or a array to be received */
4790     k         = 0;
4791     for (i=0; i<nrecvs; i++) {
4792       rowlen = rvalues + rstarts[i]*rbs;
4793       nrows  = rbs*(rstarts[i+1]-rstarts[i]); /* num of rows to be received */
4794       for (j=0; j<nrows; j++) {
4795         b_othi[k+1] = b_othi[k] + rowlen[j];
4796         ierr = PetscIntSumError(rowlen[j],len,&len);CHKERRQ(ierr);
4797         k++;
4798       }
4799       rstartsj[i+1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
4800     }
4801     ierr = PetscFree(rvalues);CHKERRQ(ierr);
4802 
4803     /* allocate space for j and a arrrays of B_oth */
4804     ierr = PetscMalloc1(b_othi[aBn]+1,&b_othj);CHKERRQ(ierr);
4805     ierr = PetscMalloc1(b_othi[aBn]+1,&b_otha);CHKERRQ(ierr);
4806 
4807     /* j-array */
4808     /*---------*/
4809     /*  post receives of j-array */
4810     for (i=0; i<nrecvs; i++) {
4811       nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4812       ierr  = MPI_Irecv(b_othj+rstartsj[i],nrows,MPIU_INT,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4813     }
4814 
4815     /* pack the outgoing message j-array */
4816     k = 0;
4817     for (i=0; i<nsends; i++) {
4818       nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4819       bufJ  = bufj+sstartsj[i];
4820       for (j=0; j<nrows; j++) {
4821         row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4822         for (ll=0; ll<sbs; ll++) {
4823           ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4824           for (l=0; l<ncols; l++) {
4825             *bufJ++ = cols[l];
4826           }
4827           ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,&cols,NULL);CHKERRQ(ierr);
4828         }
4829       }
4830       ierr = MPI_Isend(bufj+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_INT,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4831     }
4832 
4833     /* recvs and sends of j-array are completed */
4834     i = nrecvs;
4835     while (i--) {
4836       ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4837     }
4838     if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4839   } else if (scall == MAT_REUSE_MATRIX) {
4840     sstartsj = *startsj_s;
4841     rstartsj = *startsj_r;
4842     bufa     = *bufa_ptr;
4843     b_oth    = (Mat_SeqAIJ*)(*B_oth)->data;
4844     b_otha   = b_oth->a;
4845   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not posses an object container");
4846 
4847   /* a-array */
4848   /*---------*/
4849   /*  post receives of a-array */
4850   for (i=0; i<nrecvs; i++) {
4851     nrows = rstartsj[i+1]-rstartsj[i]; /* length of the msg received */
4852     ierr  = MPI_Irecv(b_otha+rstartsj[i],nrows,MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);CHKERRQ(ierr);
4853   }
4854 
4855   /* pack the outgoing message a-array */
4856   k = 0;
4857   for (i=0; i<nsends; i++) {
4858     nrows = sstarts[i+1]-sstarts[i]; /* num of block rows */
4859     bufA  = bufa+sstartsj[i];
4860     for (j=0; j<nrows; j++) {
4861       row = srow[k++] + B->rmap->range[rank];  /* global row idx */
4862       for (ll=0; ll<sbs; ll++) {
4863         ierr = MatGetRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4864         for (l=0; l<ncols; l++) {
4865           *bufA++ = vals[l];
4866         }
4867         ierr = MatRestoreRow_MPIAIJ(B,row+ll,&ncols,NULL,&vals);CHKERRQ(ierr);
4868       }
4869     }
4870     ierr = MPI_Isend(bufa+sstartsj[i],sstartsj[i+1]-sstartsj[i],MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);CHKERRQ(ierr);
4871   }
4872   /* recvs and sends of a-array are completed */
4873   i = nrecvs;
4874   while (i--) {
4875     ierr = MPI_Waitany(nrecvs,rwaits,&jj,&rstatus);CHKERRQ(ierr);
4876   }
4877   if (nsends) {ierr = MPI_Waitall(nsends,swaits,sstatus);CHKERRQ(ierr);}
4878   ierr = PetscFree2(rwaits,swaits);CHKERRQ(ierr);
4879 
4880   if (scall == MAT_INITIAL_MATRIX) {
4881     /* put together the new matrix */
4882     ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,aBn,B->cmap->N,b_othi,b_othj,b_otha,B_oth);CHKERRQ(ierr);
4883 
4884     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
4885     /* Since these are PETSc arrays, change flags to free them as necessary. */
4886     b_oth          = (Mat_SeqAIJ*)(*B_oth)->data;
4887     b_oth->free_a  = PETSC_TRUE;
4888     b_oth->free_ij = PETSC_TRUE;
4889     b_oth->nonew   = 0;
4890 
4891     ierr = PetscFree(bufj);CHKERRQ(ierr);
4892     if (!startsj_s || !bufa_ptr) {
4893       ierr = PetscFree2(sstartsj,rstartsj);CHKERRQ(ierr);
4894       ierr = PetscFree(bufa_ptr);CHKERRQ(ierr);
4895     } else {
4896       *startsj_s = sstartsj;
4897       *startsj_r = rstartsj;
4898       *bufa_ptr  = bufa;
4899     }
4900   }
4901   ierr = PetscLogEventEnd(MAT_GetBrowsOfAocols,A,B,0,0);CHKERRQ(ierr);
4902   PetscFunctionReturn(0);
4903 }
4904 
4905 /*@C
4906   MatGetCommunicationStructs - Provides access to the communication structures used in matrix-vector multiplication.
4907 
4908   Not Collective
4909 
4910   Input Parameters:
4911 . A - The matrix in mpiaij format
4912 
4913   Output Parameter:
4914 + lvec - The local vector holding off-process values from the argument to a matrix-vector product
4915 . colmap - A map from global column index to local index into lvec
4916 - multScatter - A scatter from the argument of a matrix-vector product to lvec
4917 
4918   Level: developer
4919 
4920 @*/
4921 #if defined(PETSC_USE_CTABLE)
4922 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscTable *colmap, VecScatter *multScatter)
4923 #else
4924 PetscErrorCode  MatGetCommunicationStructs(Mat A, Vec *lvec, PetscInt *colmap[], VecScatter *multScatter)
4925 #endif
4926 {
4927   Mat_MPIAIJ *a;
4928 
4929   PetscFunctionBegin;
4930   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
4931   PetscValidPointer(lvec, 2);
4932   PetscValidPointer(colmap, 3);
4933   PetscValidPointer(multScatter, 4);
4934   a = (Mat_MPIAIJ*) A->data;
4935   if (lvec) *lvec = a->lvec;
4936   if (colmap) *colmap = a->colmap;
4937   if (multScatter) *multScatter = a->Mvctx;
4938   PetscFunctionReturn(0);
4939 }
4940 
4941 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat,MatType,MatReuse,Mat*);
4942 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat,MatType,MatReuse,Mat*);
4943 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat,MatType,MatReuse,Mat*);
4944 #if defined(PETSC_HAVE_ELEMENTAL)
4945 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat,MatType,MatReuse,Mat*);
4946 #endif
4947 #if defined(PETSC_HAVE_HYPRE)
4948 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat,MatType,MatReuse,Mat*);
4949 PETSC_INTERN PetscErrorCode MatMatMatMult_Transpose_AIJ_AIJ(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
4950 #endif
4951 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_IS(Mat,MatType,MatReuse,Mat*);
4952 
4953 /*
4954     Computes (B'*A')' since computing B*A directly is untenable
4955 
4956                n                       p                          p
4957         (              )       (              )         (                  )
4958       m (      A       )  *  n (       B      )   =   m (         C        )
4959         (              )       (              )         (                  )
4960 
4961 */
4962 PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A,Mat B,Mat C)
4963 {
4964   PetscErrorCode ierr;
4965   Mat            At,Bt,Ct;
4966 
4967   PetscFunctionBegin;
4968   ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
4969   ierr = MatTranspose(B,MAT_INITIAL_MATRIX,&Bt);CHKERRQ(ierr);
4970   ierr = MatMatMult(Bt,At,MAT_INITIAL_MATRIX,1.0,&Ct);CHKERRQ(ierr);
4971   ierr = MatDestroy(&At);CHKERRQ(ierr);
4972   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
4973   ierr = MatTranspose(Ct,MAT_REUSE_MATRIX,&C);CHKERRQ(ierr);
4974   ierr = MatDestroy(&Ct);CHKERRQ(ierr);
4975   PetscFunctionReturn(0);
4976 }
4977 
4978 PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
4979 {
4980   PetscErrorCode ierr;
4981   PetscInt       m=A->rmap->n,n=B->cmap->n;
4982   Mat            Cmat;
4983 
4984   PetscFunctionBegin;
4985   if (A->cmap->n != B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"A->cmap->n %d != B->rmap->n %d\n",A->cmap->n,B->rmap->n);
4986   ierr = MatCreate(PetscObjectComm((PetscObject)A),&Cmat);CHKERRQ(ierr);
4987   ierr = MatSetSizes(Cmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
4988   ierr = MatSetBlockSizesFromMats(Cmat,A,B);CHKERRQ(ierr);
4989   ierr = MatSetType(Cmat,MATMPIDENSE);CHKERRQ(ierr);
4990   ierr = MatMPIDenseSetPreallocation(Cmat,NULL);CHKERRQ(ierr);
4991   ierr = MatAssemblyBegin(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4992   ierr = MatAssemblyEnd(Cmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
4993 
4994   Cmat->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
4995 
4996   *C = Cmat;
4997   PetscFunctionReturn(0);
4998 }
4999 
5000 /* ----------------------------------------------------------------*/
5001 PETSC_INTERN PetscErrorCode MatMatMult_MPIDense_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
5002 {
5003   PetscErrorCode ierr;
5004 
5005   PetscFunctionBegin;
5006   if (scall == MAT_INITIAL_MATRIX) {
5007     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5008     ierr = MatMatMultSymbolic_MPIDense_MPIAIJ(A,B,fill,C);CHKERRQ(ierr);
5009     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
5010   }
5011   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5012   ierr = MatMatMultNumeric_MPIDense_MPIAIJ(A,B,*C);CHKERRQ(ierr);
5013   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
5014   PetscFunctionReturn(0);
5015 }
5016 
5017 /*MC
5018    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
5019 
5020    Options Database Keys:
5021 . -mat_type mpiaij - sets the matrix type to "mpiaij" during a call to MatSetFromOptions()
5022 
5023   Level: beginner
5024 
5025 .seealso: MatCreateAIJ()
5026 M*/
5027 
5028 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
5029 {
5030   Mat_MPIAIJ     *b;
5031   PetscErrorCode ierr;
5032   PetscMPIInt    size;
5033 
5034   PetscFunctionBegin;
5035   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)B),&size);CHKERRQ(ierr);
5036 
5037   ierr          = PetscNewLog(B,&b);CHKERRQ(ierr);
5038   B->data       = (void*)b;
5039   ierr          = PetscMemcpy(B->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);
5040   B->assembled  = PETSC_FALSE;
5041   B->insertmode = NOT_SET_VALUES;
5042   b->size       = size;
5043 
5044   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)B),&b->rank);CHKERRQ(ierr);
5045 
5046   /* build cache for off array entries formed */
5047   ierr = MatStashCreate_Private(PetscObjectComm((PetscObject)B),1,&B->stash);CHKERRQ(ierr);
5048 
5049   b->donotstash  = PETSC_FALSE;
5050   b->colmap      = 0;
5051   b->garray      = 0;
5052   b->roworiented = PETSC_TRUE;
5053 
5054   /* stuff used for matrix vector multiply */
5055   b->lvec  = NULL;
5056   b->Mvctx = NULL;
5057 
5058   /* stuff for MatGetRow() */
5059   b->rowindices   = 0;
5060   b->rowvalues    = 0;
5061   b->getrowactive = PETSC_FALSE;
5062 
5063   /* flexible pointer used in CUSP/CUSPARSE classes */
5064   b->spptr = NULL;
5065 
5066   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetUseScalableIncreaseOverlap_C",MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ);CHKERRQ(ierr);
5067   ierr = PetscObjectComposeFunction((PetscObject)B,"MatStoreValues_C",MatStoreValues_MPIAIJ);CHKERRQ(ierr);
5068   ierr = PetscObjectComposeFunction((PetscObject)B,"MatRetrieveValues_C",MatRetrieveValues_MPIAIJ);CHKERRQ(ierr);
5069   ierr = PetscObjectComposeFunction((PetscObject)B,"MatIsTranspose_C",MatIsTranspose_MPIAIJ);CHKERRQ(ierr);
5070   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocation_C",MatMPIAIJSetPreallocation_MPIAIJ);CHKERRQ(ierr);
5071   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMPIAIJSetPreallocationCSR_C",MatMPIAIJSetPreallocationCSR_MPIAIJ);CHKERRQ(ierr);
5072   ierr = PetscObjectComposeFunction((PetscObject)B,"MatDiagonalScaleLocal_C",MatDiagonalScaleLocal_MPIAIJ);CHKERRQ(ierr);
5073   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijperm_C",MatConvert_MPIAIJ_MPIAIJPERM);CHKERRQ(ierr);
5074   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpiaijcrl_C",MatConvert_MPIAIJ_MPIAIJCRL);CHKERRQ(ierr);
5075   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_mpisbaij_C",MatConvert_MPIAIJ_MPISBAIJ);CHKERRQ(ierr);
5076 #if defined(PETSC_HAVE_ELEMENTAL)
5077   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_elemental_C",MatConvert_MPIAIJ_Elemental);CHKERRQ(ierr);
5078 #endif
5079 #if defined(PETSC_HAVE_HYPRE)
5080   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_hypre_C",MatConvert_AIJ_HYPRE);CHKERRQ(ierr);
5081 #endif
5082   ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpiaij_is_C",MatConvert_MPIAIJ_IS);CHKERRQ(ierr);
5083   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_mpidense_mpiaij_C",MatMatMult_MPIDense_MPIAIJ);CHKERRQ(ierr);
5084   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_mpidense_mpiaij_C",MatMatMultSymbolic_MPIDense_MPIAIJ);CHKERRQ(ierr);
5085   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_mpidense_mpiaij_C",MatMatMultNumeric_MPIDense_MPIAIJ);CHKERRQ(ierr);
5086 #if defined(PETSC_HAVE_HYPRE)
5087   ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMatMult_transpose_mpiaij_mpiaij_C",MatMatMatMult_Transpose_AIJ_AIJ);CHKERRQ(ierr);
5088 #endif
5089   ierr = PetscObjectChangeTypeName((PetscObject)B,MATMPIAIJ);CHKERRQ(ierr);
5090   PetscFunctionReturn(0);
5091 }
5092 
5093 /*@C
5094      MatCreateMPIAIJWithSplitArrays - creates a MPI AIJ matrix using arrays that contain the "diagonal"
5095          and "off-diagonal" part of the matrix in CSR format.
5096 
5097    Collective on MPI_Comm
5098 
5099    Input Parameters:
5100 +  comm - MPI communicator
5101 .  m - number of local rows (Cannot be PETSC_DECIDE)
5102 .  n - This value should be the same as the local size used in creating the
5103        x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have
5104        calculated if N is given) For square matrices n is almost always m.
5105 .  M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
5106 .  N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
5107 .   i - row indices for "diagonal" portion of matrix
5108 .   j - column indices
5109 .   a - matrix values
5110 .   oi - row indices for "off-diagonal" portion of matrix
5111 .   oj - column indices
5112 -   oa - matrix values
5113 
5114    Output Parameter:
5115 .   mat - the matrix
5116 
5117    Level: advanced
5118 
5119    Notes:
5120        The i, j, and a arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
5121        must free the arrays once the matrix has been destroyed and not before.
5122 
5123        The i and j indices are 0 based
5124 
5125        See MatCreateAIJ() for the definition of "diagonal" and "off-diagonal" portion of the matrix
5126 
5127        This sets local rows and cannot be used to set off-processor values.
5128 
5129        Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
5130        legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
5131        not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
5132        the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
5133        keep track of the underlying array. Use MatSetOption(A,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) to disable all
5134        communication if it is known that only local entries will be set.
5135 
5136 .keywords: matrix, aij, compressed row, sparse, parallel
5137 
5138 .seealso: MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatMPIAIJSetPreallocation(), MatMPIAIJSetPreallocationCSR(),
5139           MATMPIAIJ, MatCreateAIJ(), MatCreateMPIAIJWithArrays()
5140 @*/
5141 PetscErrorCode  MatCreateMPIAIJWithSplitArrays(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt i[],PetscInt j[],PetscScalar a[],PetscInt oi[], PetscInt oj[],PetscScalar oa[],Mat *mat)
5142 {
5143   PetscErrorCode ierr;
5144   Mat_MPIAIJ     *maij;
5145 
5146   PetscFunctionBegin;
5147   if (m < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"local number of rows (m) cannot be PETSC_DECIDE, or negative");
5148   if (i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
5149   if (oi[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"oi (row indices) must start with 0");
5150   ierr = MatCreate(comm,mat);CHKERRQ(ierr);
5151   ierr = MatSetSizes(*mat,m,n,M,N);CHKERRQ(ierr);
5152   ierr = MatSetType(*mat,MATMPIAIJ);CHKERRQ(ierr);
5153   maij = (Mat_MPIAIJ*) (*mat)->data;
5154 
5155   (*mat)->preallocated = PETSC_TRUE;
5156 
5157   ierr = PetscLayoutSetUp((*mat)->rmap);CHKERRQ(ierr);
5158   ierr = PetscLayoutSetUp((*mat)->cmap);CHKERRQ(ierr);
5159 
5160   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,i,j,a,&maij->A);CHKERRQ(ierr);
5161   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,(*mat)->cmap->N,oi,oj,oa,&maij->B);CHKERRQ(ierr);
5162 
5163   ierr = MatAssemblyBegin(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5164   ierr = MatAssemblyEnd(maij->A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5165   ierr = MatAssemblyBegin(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5166   ierr = MatAssemblyEnd(maij->B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5167 
5168   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
5169   ierr = MatAssemblyBegin(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5170   ierr = MatAssemblyEnd(*mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
5171   ierr = MatSetOption(*mat,MAT_NO_OFF_PROC_ENTRIES,PETSC_FALSE);CHKERRQ(ierr);
5172   ierr = MatSetOption(*mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
5173   PetscFunctionReturn(0);
5174 }
5175 
5176 /*
5177     Special version for direct calls from Fortran
5178 */
5179 #include <petsc/private/fortranimpl.h>
5180 
5181 /* Change these macros so can be used in void function */
5182 #undef CHKERRQ
5183 #define CHKERRQ(ierr) CHKERRABORT(PETSC_COMM_WORLD,ierr)
5184 #undef SETERRQ2
5185 #define SETERRQ2(comm,ierr,b,c,d) CHKERRABORT(comm,ierr)
5186 #undef SETERRQ3
5187 #define SETERRQ3(comm,ierr,b,c,d,e) CHKERRABORT(comm,ierr)
5188 #undef SETERRQ
5189 #define SETERRQ(c,ierr,b) CHKERRABORT(c,ierr)
5190 
5191 #if defined(PETSC_HAVE_FORTRAN_CAPS)
5192 #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
5193 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
5194 #define matsetvaluesmpiaij_ matsetvaluesmpiaij
5195 #else
5196 #endif
5197 PETSC_EXTERN void PETSC_STDCALL matsetvaluesmpiaij_(Mat *mmat,PetscInt *mm,const PetscInt im[],PetscInt *mn,const PetscInt in[],const PetscScalar v[],InsertMode *maddv,PetscErrorCode *_ierr)
5198 {
5199   Mat            mat  = *mmat;
5200   PetscInt       m    = *mm, n = *mn;
5201   InsertMode     addv = *maddv;
5202   Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)mat->data;
5203   PetscScalar    value;
5204   PetscErrorCode ierr;
5205 
5206   MatCheckPreallocated(mat,1);
5207   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
5208 
5209 #if defined(PETSC_USE_DEBUG)
5210   else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
5211 #endif
5212   {
5213     PetscInt  i,j,rstart  = mat->rmap->rstart,rend = mat->rmap->rend;
5214     PetscInt  cstart      = mat->cmap->rstart,cend = mat->cmap->rend,row,col;
5215     PetscBool roworiented = aij->roworiented;
5216 
5217     /* Some Variables required in the macro */
5218     Mat        A                 = aij->A;
5219     Mat_SeqAIJ *a                = (Mat_SeqAIJ*)A->data;
5220     PetscInt   *aimax            = a->imax,*ai = a->i,*ailen = a->ilen,*aj = a->j;
5221     MatScalar  *aa               = a->a;
5222     PetscBool  ignorezeroentries = (((a->ignorezeroentries)&&(addv==ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
5223     Mat        B                 = aij->B;
5224     Mat_SeqAIJ *b                = (Mat_SeqAIJ*)B->data;
5225     PetscInt   *bimax            = b->imax,*bi = b->i,*bilen = b->ilen,*bj = b->j,bm = aij->B->rmap->n,am = aij->A->rmap->n;
5226     MatScalar  *ba               = b->a;
5227 
5228     PetscInt  *rp1,*rp2,ii,nrow1,nrow2,_i,rmax1,rmax2,N,low1,high1,low2,high2,t,lastcol1,lastcol2;
5229     PetscInt  nonew = a->nonew;
5230     MatScalar *ap1,*ap2;
5231 
5232     PetscFunctionBegin;
5233     for (i=0; i<m; i++) {
5234       if (im[i] < 0) continue;
5235 #if defined(PETSC_USE_DEBUG)
5236       if (im[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",im[i],mat->rmap->N-1);
5237 #endif
5238       if (im[i] >= rstart && im[i] < rend) {
5239         row      = im[i] - rstart;
5240         lastcol1 = -1;
5241         rp1      = aj + ai[row];
5242         ap1      = aa + ai[row];
5243         rmax1    = aimax[row];
5244         nrow1    = ailen[row];
5245         low1     = 0;
5246         high1    = nrow1;
5247         lastcol2 = -1;
5248         rp2      = bj + bi[row];
5249         ap2      = ba + bi[row];
5250         rmax2    = bimax[row];
5251         nrow2    = bilen[row];
5252         low2     = 0;
5253         high2    = nrow2;
5254 
5255         for (j=0; j<n; j++) {
5256           if (roworiented) value = v[i*n+j];
5257           else value = v[i+j*m];
5258           if (in[j] >= cstart && in[j] < cend) {
5259             col = in[j] - cstart;
5260             if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5261             MatSetValues_SeqAIJ_A_Private(row,col,value,addv,im[i],in[j]);
5262           } else if (in[j] < 0) continue;
5263 #if defined(PETSC_USE_DEBUG)
5264           else if (in[j] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[j],mat->cmap->N-1);
5265 #endif
5266           else {
5267             if (mat->was_assembled) {
5268               if (!aij->colmap) {
5269                 ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
5270               }
5271 #if defined(PETSC_USE_CTABLE)
5272               ierr = PetscTableFind(aij->colmap,in[j]+1,&col);CHKERRQ(ierr);
5273               col--;
5274 #else
5275               col = aij->colmap[in[j]] - 1;
5276 #endif
5277               if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && row != col) continue;
5278               if (col < 0 && !((Mat_SeqAIJ*)(aij->A->data))->nonew) {
5279                 ierr = MatDisAssemble_MPIAIJ(mat);CHKERRQ(ierr);
5280                 col  =  in[j];
5281                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
5282                 B     = aij->B;
5283                 b     = (Mat_SeqAIJ*)B->data;
5284                 bimax = b->imax; bi = b->i; bilen = b->ilen; bj = b->j;
5285                 rp2   = bj + bi[row];
5286                 ap2   = ba + bi[row];
5287                 rmax2 = bimax[row];
5288                 nrow2 = bilen[row];
5289                 low2  = 0;
5290                 high2 = nrow2;
5291                 bm    = aij->B->rmap->n;
5292                 ba    = b->a;
5293               }
5294             } else col = in[j];
5295             MatSetValues_SeqAIJ_B_Private(row,col,value,addv,im[i],in[j]);
5296           }
5297         }
5298       } else if (!aij->donotstash) {
5299         if (roworiented) {
5300           ierr = MatStashValuesRow_Private(&mat->stash,im[i],n,in,v+i*n,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5301         } else {
5302           ierr = MatStashValuesCol_Private(&mat->stash,im[i],n,in,v+i,m,(PetscBool)(ignorezeroentries && (addv == ADD_VALUES)));CHKERRQ(ierr);
5303         }
5304       }
5305     }
5306   }
5307   PetscFunctionReturnVoid();
5308 }
5309 
5310